Do females and males differ in organ scaling?

This supplementary file contains the R code for processing and analysing the raw data, and creating figures for the manuscript - Do females and males differ in organ scaling? A mechanistic approach and a phylogenetic multilevel analysis across vertebrates

Data subset used in this study is part of a database on organ sizes, which is available here: https://felixpleiva.github.io/organ_size_DB/. Additionally, I complemented the dataset on organ size by revisiting a recent publication by Tsuboi et al., 2018, which includes, among other information, sex- and species-specific data on organ size for numerous species of mammals, birds, and fish. Together, these approaches, allowed us to compile information for 204 vertebrate species and data on a total of 9 different organs.

# Clean working environment
rm(list = ls())

Licence

This repository is provided by the authors under the Attribution-NonCommercial-NoDerivatives 4.0 International licence

Citation

When using the data and/or code associated with this repository, they must be cited as follows:

Leiva, F. P., A. J. Hendriks. (2026). Do females and males differ in organ scaling? A mechanistic approach and a phylogenetic multilevel analysis across vertebrates. Zenodo. pending DOI.

Contact

This script is authored by Félix P. Leiva. For any questions related to this resource, please contact me at the email address: felixpleiva@gmail.com.

Load and tidy data

dat <- read_xlsx("../outputs/dat_for_analyses_full_merged.xlsx") %>%
  rename( 
    sex = sex_individual,
    life_stage = life_stage_individual,
    original_category = trait_size_category,
    body_size = body_size_mean,
    organ_size = organ_size_mean,
    species = species_reported
  ) %>%
  mutate(organ_grouped = recode(organ_grouped,
                                pituitary_gland = "pituitary_glands",
                                lung = "lungs",
                                kidney = "kidneys")) %>%
  mutate(class = recode(class,
                        Actinopterygii = "Teleostei"))


# Calculate mean per species and sex. Most species were represented primarily by adults. Life stages that were not explicitly reported were assumed to correspond to adult individuals.

dat_mean <- dat %>%
  group_by(
    phylum, class, order, family, genus,
    species, sex, organ_grouped
  ) %>%
  summarise(
    body_size = mean(body_size, na.rm = TRUE),
    organ_size = mean(organ_size, na.rm = TRUE),
    .groups = "drop"
  ) %>%
  mutate(
    log10_body_size = log10(body_size),
    log10_organ_size = log10(organ_size),
    phylo = gsub(" ", "_", species)
  )

Next, from the preceding code, I will extract the list of species for which I want to retrieve the phylogenetic tree and export it to my working directory.

list_of_species <- dat_mean %>%
  distinct(species) %>%
  pull(species) %>%
  as.character()

writeLines(list_of_species, "../outputs/list_of_species.txt")

Now I have exported the list of species, I will visit the TimeTree of Life website and, in the lower section labelled Load a list of species, upload the file list_of_species.csv. Subsequently, I will export it in Newick format. Note that not all species from our list are included in the resulting tree, although most are represented.

Check data structure and transform variables if necessary

glimpse(dat_mean)

Rows: 676
Columns: 13
$ phylum           <chr> "Chordata", "Chordata", "Chordata", "Chordata", "Chor…
$ class            <chr> "Aves", "Aves", "Aves", "Aves", "Aves", "Aves", "Aves…
$ order            <chr> "Anseriformes", "Anseriformes", "Anseriformes", "Anse…
$ family           <chr> "Anatidae", "Anatidae", "Anatidae", "Anatidae", "Anat…
$ genus            <chr> "Anas", "Anas", "Anas", "Anas", "Anas", "Anas", "Anas…
$ species          <chr> "Anas acuta", "Anas acuta", "Anas crecca", "Anas crec…
$ sex              <chr> "female", "male", "female", "male", "female", "female…
$ organ_grouped    <chr> "brain", "brain", "brain", "brain", "adrenal_glands",…
$ body_size        <dbl> 721, 1176, 279, 347, 2921, 1200, 2921, 2921, 2921, 29…
$ organ_size       <dbl> 4.91, 5.28, 3.18, 2.90, 0.13, 5.44, 19.50, 17.40, 3.5…
$ log10_body_size  <dbl> 2.9, 3.1, 2.4, 2.5, 3.5, 3.1, 3.5, 3.5, 3.5, 3.5, 3.5…
$ log10_organ_size <dbl> 0.691, 0.723, 0.503, 0.463, -0.886, 0.736, 1.290, 1.2…
$ phylo            <chr> "Anas_acuta", "Anas_acuta", "Anas_crecca", "Anas_crec…

Variables to convert to factor

columns_to_factor <- c(
  "phylum", 
  "class", 
  "order", 
  "family", 
  "genus", 
  "species",
  "phylo",   
  "sex",
  "organ_grouped"
)

Variables to convert to numeric

columns_to_numeric <- c(
  "body_size", 
  "organ_size",
  "log10_organ_size",
  "log10_body_size"
)

Apply transformation

# Apply the conversions to the dataset.
dat_mean <- dat_mean %>%
  mutate(
    across(all_of(columns_to_factor), as.factor),
    across(all_of(columns_to_numeric), as.numeric)
  )

# Confirm that changes have been applied correctly
glimpse(dat_mean)

Rows: 676
Columns: 13
$ phylum           <fct> Chordata, Chordata, Chordata, Chordata, Chordata, Cho…
$ class            <fct> Aves, Aves, Aves, Aves, Aves, Aves, Aves, Aves, Aves,…
$ order            <fct> Anseriformes, Anseriformes, Anseriformes, Anseriforme…
$ family           <fct> Anatidae, Anatidae, Anatidae, Anatidae, Anatidae, Ana…
$ genus            <fct> Anas, Anas, Anas, Anas, Anas, Anas, Anas, Anas, Anas,…
$ species          <fct> Anas acuta, Anas acuta, Anas crecca, Anas crecca, Ana…
$ sex              <fct> female, male, female, male, female, female, female, f…
$ organ_grouped    <fct> brain, brain, brain, brain, adrenal_glands, brain, he…
$ body_size        <dbl> 721, 1176, 279, 347, 2921, 1200, 2921, 2921, 2921, 29…
$ organ_size       <dbl> 4.91, 5.28, 3.18, 2.90, 0.13, 5.44, 19.50, 17.40, 3.5…
$ log10_body_size  <dbl> 2.9, 3.1, 2.4, 2.5, 3.5, 3.1, 3.5, 3.5, 3.5, 3.5, 3.5…
$ log10_organ_size <dbl> 0.691, 0.723, 0.503, 0.463, -0.886, 0.736, 1.290, 1.2…
$ phylo            <fct> Anas_acuta, Anas_acuta, Anas_crecca, Anas_crecca, Ana…

Filter the dataframe to include only organs with at least five species per sex and organ. Some of them have only three species per sex. From this output, the thymus, large intestine, and small intestine are excluded.

# First identify qualifying organ-sex combinations
organs_five_species <- dat_mean %>%
  count(organ_grouped, species, sex) %>%
  group_by(organ_grouped, sex) %>% # by sex and organ
  summarise(n_species = n_distinct(species), .groups = "drop") %>%
  filter(n_species >= 5) # at least 5 spp 

# Then filter original data to these combinations only
dat_mean <- dat_mean %>%
  inner_join(organs_five_species %>% select(organ_grouped, sex), 
             by = c("organ_grouped", "sex"))

# Lets check whcih organs were retained after this filter
dat_mean %>%
  summarise(n_species = n_distinct(species), .by = organ_grouped)

# A tibble: 10 × 2
   organ_grouped    n_species
   <fct>                <int>
 1 brain                  246
 2 adrenal_glands           7
 3 heart                   12
 4 kidneys                  8
 5 liver                   14
 6 pancreas                 6
 7 spleen                  11
 8 stomach                  8
 9 pituitary_glands         7
10 lungs                    8

In addition to the five-species filter, we applied a ten-species filter when the organ in question was the brain. This was done to make our analyses more comparable to those recently published by Tsuboi et al. (2018). Moreover, this approach allowed us to assess the robustness and granularity of our results within a subset of species for which more data were available. The ten-species filter encompassed a total of two families of fish, five families of birds, and three families of mammals.

# Identify qualifying families (>10 unique species per family) for brain only
good_families_brain <- dat_mean %>%
  filter(organ_grouped == "brain") %>%
  group_by(family) %>%
  summarise(n_species = n_distinct(species), .groups = "drop") %>%
  filter(n_species > 10) %>%
  pull(family)

# Filter main dataset: keep ALL non-brain data + brain data for qualifying families only
dat_mean<- dat_mean %>%
  filter(organ_grouped != "brain" | family %in% good_families_brain) %>%
  droplevels() # here i drop the rows filtered out

# Species counts per organ, class, order, family
species_summary <- dat_mean %>%
  distinct(organ_grouped, class, order, family, species, .keep_all = TRUE) %>%
  count(organ_grouped, class, order, family, name = "n_species_unique") %>%
  arrange(organ_grouped, class, desc(n_species_unique))

One of the things I discovered recently is the library (DT), which enables the creation of these interactive tables that allow for much more dynamic filtering. Super cool!

datatable(
  species_summary,
  filter = "top", 
  options = list(
    pageLength = 15,
    autoWidth = TRUE,
    dom = 'Bfrtip', 
    buttons = c('copy', 'csv', 'excel')
  ),
  colnames = c("Organ", "Class", "Order", "Family", "Species count")
)

Load and prune phylogenetic tree

tree <- read.tree("../outputs/phylogenetic_tree.nwk")

# Number of tips (species)
length(tree$tip.label)

[1] 277

Our next step is to prune the tree to retain only those species for which organ size measurements exist for both males and females. This pruning is important because our phylogenetic informed analyses require the calculation of a variance-covariance matrix based on the shared evolutionary history of the species.

# Check for database/tree species mismatches
setdiff(tree$tip.label, dat_mean$phylo)      # Tree species absent in database

 [1] "Pseudosimochromis_babaulti"            
 [2] "Oostethus_brachyurus"                  
 [3] "Dunckerocampus_dactyliophorus"         
 [4] "Madoqua_kirkii"                        
 [5] "Philantomba_monticola"                 
 [6] "Aotus_trivirgatus"                     
 [7] "Cebuella_pygmaea"                      
 [8] "Callithrix_penicillata"                
 [9] "Callimico_goeldii"                     
[10] "Leontopithecus_chrysomelas"            
[11] "Leontopithecus_rosalia"                
[12] "Leontocebus_fuscicollis_illigeri"      
[13] "Saguinus_mystax"                       
[14] "Saguinus_labiatus_labiatus"            
[15] "Saguinus_leucopus"                     
[16] "Saguinus_midas"                        
[17] "Saguinus_niger"                        
[18] "Saguinus_oedipus"                      
[19] "Saguinus_geoffroyi"                    
[20] "Cebus_olivaceus"                       
[21] "Cebus_capucinus"                       
[22] "Sapajus_xanthosternos"                 
[23] "Cebus_nigritus_robustus"               
[24] "Saimiri_sciureus_macrodon"             
[25] "Saimiri_sciureus_sciureus"             
[26] "Saimiri_sciureus_cassiquiarensis"      
[27] "Chlorocebus_pygerythrus_pygerythrus"   
[28] "Cercopithecus_mitis_stuhlmanni"        
[29] "Cercopithecus_albogularis_kolbi"       
[30] "Cercopithecus_albogularis_erythrarchus"
[31] "Cercopithecus_mona"                    
[32] "Cercopithecus_neglectus"               
[33] "Papio_hamadryas"                       
[34] "Theropithecus_gelada"                  
[35] "Macaca_radiata_radiata"                
[36] "Macaca_nemestrina"                     
[37] "Macaca_leonina"                        
[38] "Semnopithecus_entellus"                
[39] "Semnopithecus_priam"                   
[40] "Trachypithecus_vetulus_vetulus"        
[41] "Trachypithecus_phayrei_shanicus"       
[42] "Trachypithecus_phayrei_crepuscula"     
[43] "Presbytis_thomasi"                     
[44] "Presbytis_rubicunda_rubicunda"         
[45] "Presbytis_melalophos_sumatranus"       
[46] "Presbytis_femoralis_percura"           
[47] "Nasalis_larvatus"                      
[48] "Procolobus_verus"                      
[49] "Piliocolobus_tephrosceles"             
[50] "Piliocolobus_kirkii"                   
[51] "Colobus_vellerosus"                    
[52] "Colobus_polykomos"                     
[53] "Colobus_angolensis_palliatus"          
[54] "Psephotellus_varius"                   
[55] "Orthopsittaca_manilatus"               
[56] "Lophochroa_leadbeateri"                
[57] "Zanda_funerea"                         
[58] "Crithagra_dorsostriata"                
[59] "Crithagra_burtoni"                     
[60] "Bathilda_ruficauda"                    
[61] "Granatina_ianthinogaster"              
[62] "Chloebia_gouldiae"                     
[63] "Spinus_spinus"                         
[64] "Linaria_cannabina"                     
[65] "Crithagra_mozambica"                   
[66] "Spinus_cucullatus"                     
[67] "Acanthis_flammea"                      
[68] "Chloris_spinoides"                     
[69] "Chloris_ambigua"                       
[70] "Chloris_chloris"                       
[71] "Aythya_fuligula"                       
[72] "Tetrastes_bonasia"                     
[73] "Gallus_lafayettii"                     

setdiff(dat_mean$phylo, tree$tip.label)      # Database species absent in tree

 [1] "Nyroca_fuligula"              "Ammoperdix_griseogularis"    
 [3] "Bonasa_bonasia"               "Gallus_lafayetii"            
 [5] "Lagopus_mutus"                "Erythrura_gouldiae"          
 [7] "Lonchura_grandis"             "Lonchura_molucca"            
 [9] "Lonchura_pallida"             "Lonchura_quinticolor"        
[11] "Lonchura_spectabilis"         "Lonchura_tristissima"        
[13] "Mandingoa_nitidula"           "Neochmia_ruficauda"          
[15] "Pyrenestes_ostrinus"          "Uraeginthus_ianthinogaster"  
[17] "Carduelis_ambigua"            "Carduelis_cannabina"         
[19] "Carduelis_chloris"            "Carduelis_cucullata"         
[21] "Carduelis_flammea"            "Carduelis_spinoides"         
[23] "Carduelis_spinus"             "Serinus_burtoni"             
[25] "Serinus_dorsostriatus"        "Serinus_mozambicus"          
[27] "Cacatua_leadbeateri"          "Calyptorhynchus_funereus"    
[29] "Orthopsittaca_manilata"       "Polytelis_swainsonii"        
[31] "Psephotus_varius"             "Cephalophus_monticola"       
[33] "Eudorcas_thomsoni"            "Madoqua_kirki"               
[35] "Saimiri_sciureus"             "Chlorocebus_aethiops_sabaeus"
[37] "Simochromis_babaulti"         "Doryichthys_martensi"        
[39] "Doryrhamphus_dactyliophorus"  "Microphis_brachyurus"        
[41] "Trachyhampus_serratus"       

# Exclude mismatched species for consistency
tree <- keep.tip(tree, intersect(tree$tip.label, dat_mean$phylo))
dat_mean <- dat_mean[dat_mean$phylo %in% tree$tip.label, ]

# Re-check for mismatches after pruning
setdiff(tree$tip.label, dat_mean$phylo)

character(0)

setdiff(dat_mean$phylo, tree$tip.label)

character(0)

# Is ultrametric?
is.ultrametric(tree)

[1] TRUE

# how many species?
length(tree$tip.label)

[1] 204

# Compute phylogenetic covariance matrix (Brownian motion)
A <- vcv.phylo(tree, corr = TRUE)

How many species have phylogenetic information available across all taxonomic classes for the brain?

dat_mean %>%
  count(organ_grouped, species, class) %>%
  group_by(organ_grouped) %>%
  filter(organ_grouped == "brain") %>%
  summarise(
    n_species = n_distinct(species),
    .groups = 'drop'
  ) %>%
  arrange(desc(n_species))

# A tibble: 1 × 2
  organ_grouped n_species
  <fct>             <int>
1 brain               189

dat_mean %>%
  count(organ_grouped, species) %>%
  group_by(organ_grouped) %>%
  count(organ_grouped, name = "n_species") %>%
  arrange(desc(n_species))

# A tibble: 10 × 2
# Groups:   organ_grouped [10]
   organ_grouped    n_species
   <fct>                <int>
 1 brain                  189
 2 liver                   12
 3 heart                   10
 4 spleen                   9
 5 stomach                  8
 6 kidneys                  6
 7 lungs                    6
 8 adrenal_glands           5
 9 pituitary_glands         5
10 pancreas                 4

Since our objective is to account for the evolutionary history of the species, it is essential to recognise that, in a comparative context, species cannot be treated as independent units of observation. Closely related species tend to exhibit similar values for a given trait due to shared ancestry. Although no strict rule exists for the minimum number of species required, Garland and Adolph’s paper Why Not to Do Two-Species Comparative Studies: Limitations on Inferring Adaptation’ discusses relevant limitations and recommends broader sampling. As a rule of thumb, we evaluated the effects of accounting for shared evolutionary history in organs measured across more than 5 species, and compared these results with non-phylogenetic models (onward refereed as simple models). It means we won´t include pancreas size in the analysis.

Exclude pancreas from the analysis (only four species)

dat_mean <- dat_mean %>% 
  filter(organ_grouped != "pancreas")

# Confirm pancreas is gone
unique(dat_mean$organ_grouped)

[1] brain            adrenal_glands   heart            kidneys         
[5] liver            spleen           stomach          pituitary_glands
[9] lungs           
10 Levels: adrenal_glands brain heart kidneys liver lungs ... stomach

And now re-run the previous lines para merge the tree and data, el cual debeiera exlcuir los datos de pancreas

# Check for database/tree species mismatches
setdiff(tree$tip.label, dat_mean$phylo)      # Tree species absent in database

character(0)

setdiff(dat_mean$phylo, tree$tip.label)      # Database species absent in tree

character(0)

# Exclude mismatched species for consistency
tree <- keep.tip(tree, intersect(tree$tip.label, dat_mean$phylo))
dat_mean <- dat_mean[dat_mean$phylo %in% tree$tip.label, ]

# Re-check for mismatches after pruning
setdiff(tree$tip.label, dat_mean$phylo)

character(0)

setdiff(dat_mean$phylo, tree$tip.label)

character(0)

# Is ultrametric?
is.ultrametric(tree)

[1] TRUE

# how many species?
length(tree$tip.label)

[1] 204

# Compute phylogenetic covariance matrix (Brownian motion)
A <- vcv.phylo(tree, corr = TRUE)

Lets count species again by organ

dat_mean %>%
  count(organ_grouped, species) %>%
  group_by(organ_grouped) %>%
  count(organ_grouped, name = "n_species") %>%
  arrange(desc(n_species))

# A tibble: 9 × 2
# Groups:   organ_grouped [9]
  organ_grouped    n_species
  <fct>                <int>
1 brain                  189
2 liver                   12
3 heart                   10
4 spleen                   9
5 stomach                  8
6 kidneys                  6
7 lungs                    6
8 adrenal_glands           5
9 pituitary_glands         5

and taxonomic Class

dat_mean %>%
  count(class, species) %>%
  group_by(class) %>%
  count(class, name = "n_species") %>%
  arrange(desc(n_species))

# A tibble: 4 × 2
# Groups:   class [4]
  class     n_species
  <fct>         <int>
1 Aves             98
2 Teleostei        70
3 Mammalia         35
4 Reptilia          1

Now the tree match the species in the dataframe, we will create a figure of the phylogenetic tree containing the 204 species for which we have organ size data for both males and females. We will add a plot indicating whether each organ was measured (green) or not (grey).

Important note!

Our analyses for most organs are based on a relatively small number of observations (i.e., species). This may limit the interpretability of our models, particularly when they are compared to one another. Model comparison using cross-validation (via the loo_compare function) was implemented in some cases following the recommendations in the cross-validation FAQ, particularly regarding influential observations. In the preceding link Aki Vehtari states: Pareto-k is also useful as a measure of influence of an observation. Highly influential observations have high k^ values. Very high k values often indicate model misspecification, outliers or mistakes in data processing. For this reason, we decided to include additional species by searching for complementary datasets. We ultimately incorporated the dataset from Tsuboi et al., which, to our knowledge, represents the most extensive available compilation of vertebrate organ (particularly brain) size data for males and females.

Figure 1

# Prepara data to merge with tree
dat_mean$organ_grouped <- gsub("_", " ", dat_mean$organ_grouped)

summary_data <- dat_mean %>%
  count(phylo, organ_grouped) %>%
  mutate(presence = if_else(n > 0, "Yes", "No")) %>%
  select(-n) %>%
  pivot_wider(
    names_from = organ_grouped,
    values_from = presence,
    values_fill = list(presence = "No")
  )

summary_data <- summary_data[summary_data$phylo %in% tree$tip.label, ]

datF_organs <- summary_data %>%
  column_to_rownames("phylo") %>%
  as.matrix()

# force matc between data and tree
datF_organs <- datF_organs[tree$tip.label, , drop = FALSE]

# Create phylogeny tree
circ <- ggtree(tree, layout = "fan", open.angle = 18) 
circ <- rotate_tree(circ, 90)

Figure_1 <- gheatmap(
  circ,
  datF_organs,
  width = 0.4, 
  offset = 0, 
  colnames_offset_x = 0, 
  colnames_offset_y = 0, 
  font.size = 2,
  hjust = 0
) +
  scale_fill_manual(values = c("grey90", "#009E73"), name = "Organ measured")  +
  theme(
    legend.position = c(0.57, 0.55), 
    legend.background = element_rect(fill = "transparent", colour = NA),
    legend.box.background = element_rect(fill = "transparent", colour = NA),
    legend.title = element_text(size = 8),      
    legend.text = element_text(size = 6),       
    legend.key.size = unit(0.8, "cm"),         
    legend.key.height = unit(0.4, "cm"),       
    legend.key.width = unit(0.4, "cm")         
  )

Figure_1

# Export figure
ggsave('../outputs/Figure_1.pdf', Figure_1, width = 7, height = 7)

Liver

Filter data and prune tree

# Filter organ of interest
dat_organ <- dat_mean %>%
  group_by(organ_grouped, sex) %>%
  ungroup() %>%
  filter(organ_grouped == "liver")

# Check for database/tree species mismatches
setdiff(tree$tip.label, dat_organ$phylo)      # Tree species absent in database

  [1] "Petrochromis_famula"             "Lobochilotes_labiatus"          
  [3] "Simochromis_diagramma"           "Petrochromis_orthognathus"      
  [5] "Ctenochromis_horei"              "Limnotilapia_dardennii"         
  [7] "Gnathochromis_pfefferi"          "Tropheus_moorii"                
  [9] "Tropheus_brichardi"              "Haplotaxodon_microlepis"        
 [11] "Perissodus_microlepis"           "Benthochromis_tricoti"          
 [13] "Cyprichromis_leptosoma"          "Greenwoodochromis_christyi"     
 [15] "Limnochromis_staneri"            "Gnathochromis_permaxillaris"    
 [17] "Baileychromis_centropomoides"    "Triglachromis_otostigma"        
 [19] "Cyphotilapia_frontosa"           "Ophthalmotilapia_ventralis"     
 [21] "Cyathopharynx_furcifer"          "Ophthalmotilapia_nasuta"        
 [23] "Ophthalmotilapia_boops"          "Aulonocranus_dewindti"          
 [25] "Ectodus_descampsii"              "Callochromis_melanostigma"      
 [27] "Xenotilapia_melanogenys"         "Xenotilapia_flavipinnis"        
 [29] "Eretmodus_cyanostictus"          "Tanganicodus_irsacae"           
 [31] "Spathodus_marlieri"              "Spathodus_erythrodon"           
 [33] "Neolamprologus_brichardi"        "Julidochromis_regani"           
 [35] "Julidochromis_marlieri"          "Neolamprologus_tetracanthus"    
 [37] "Telmatochromis_temporalis"       "Lepidiolamprologus_elongatus"   
 [39] "Lepidiolamprologus_profundicola" "Lepidiolamprologus_nkambae"     
 [41] "Altolamprologus_compressiceps"   "Neolamprologus_brevis"          
 [43] "Chalinochromis_brichardi"        "Julidochromis_ornatus"          
 [45] "Lamprologus_ornatipinnis"        "Neolamprologus_pulcher"         
 [47] "Variabilichromis_moorii"         "Neolamprologus_tretocephalus"   
 [49] "Neolamprologus_sexfasciatus"     "Trematocara_unimaculatum"       
 [51] "Hemibates_stenosoma"             "Bathybates_ferox"               
 [53] "Poecilia_reticulata"             "Nerophis_lumbriciformis"        
 [55] "Syngnathus_abaster"              "Syngnathus_schlegeli"           
 [57] "Hippocampus_comes"               "Hippocampus_trimaculatus"       
 [59] "Hippocampus_kuda"                "Hippocampus_spinosissimus"      
 [61] "Hippocampus_abdominalis"         "Hippichthys_cyanospilos"        
 [63] "Syngnathoides_biaculeatus"       "Corythoichthys_intestinalis"    
 [65] "Corythoichthys_haematopterus"    "Doryichthys_boaja"              
 [67] "Doryrhamphus_japonicus"          "Entelurus_aequoreus"            
 [69] "Syncerus_caffer"                 "Tragelaphus_eurycerus"          
 [71] "Tragelaphus_scriptus"            "Redunca_arundinum"              
 [73] "Antidorcas_marsupialis"          "Nanger_granti"                  
 [75] "Raphicerus_campestris"           "Cephalophus_natalensis"         
 [77] "Sylvicapra_grimmia"              "Oreotragus_oreotragus"          
 [79] "Hippotragus_equinus"             "Addax_nasomaculatus"            
 [81] "Oryx_gazella"                    "Connochaetes_taurinus"          
 [83] "Damaliscus_lunatus"              "Ovis_aries"                     
 [85] "Aepyceros_melampus"              "Pteropus_alecto"                
 [87] "Pteropus_poliocephalus"          "Pteropus_scapulatus"            
 [89] "Chlorocebus_aethiops"            "Chlorocebus_sabaeus"            
 [91] "Erythrocebus_patas"              "Papio_cynocephalus"             
 [93] "Papio_anubis"                    "Cercocebus_atys"                
 [95] "Macaca_arctoides"                "Macaca_mulatta"                 
 [97] "Macaca_maura"                    "Trachypithecus_francoisi"       
 [99] "Phrynocephalus_vlangalii"        "Platycercus_caledonicus"        
[101] "Platycercus_elegans"             "Platycercus_eximius"            
[103] "Platycercus_venustus"            "Barnardius_zonarius"            
[105] "Northiella_haematogaster"        "Lathamus_discolor"              
[107] "Neophema_chrysostoma"            "Neophema_pulchella"             
[109] "Psittacula_krameri"              "Eclectus_roratus"               
[111] "Aprosmictus_jonquillaceus"       "Alisterus_scapularis"           
[113] "Alisterus_amboinensis"           "Polytelis_alexandrae"           
[115] "Trichoglossus_haematodus"        "Agapornis_lilianae"             
[117] "Agapornis_taranta"               "Loriculus_vernalis"             
[119] "Ara_ararauna"                    "Guaruba_guarouba"               
[121] "Enicognathus_leptorhynchus"      "Pionites_melanocephalus"        
[123] "Forpus_coelestis"                "Forpus_passerinus"              
[125] "Amazona_leucocephala"            "Amazona_albifrons"              
[127] "Amazona_pretrei"                 "Amazona_vinacea"                
[129] "Amazona_finschi"                 "Amazona_amazonica"              
[131] "Amazona_ochrocephala"            "Amazona_aestiva"                
[133] "Brotogeris_versicolurus"         "Brotogeris_pyrrhoptera"         
[135] "Bolborhynchus_lineola"           "Poicephalus_gulielmi"           
[137] "Poicephalus_meyeri"              "Psittacus_erithacus"            
[139] "Serinus_mennelli"                "Padda_oryzivora"                
[141] "Lonchura_punctulata"             "Lonchura_flaviprymna"           
[143] "Lonchura_bicolor"                "Hypargos_niveoguttatus"         
[145] "Pytilia_hypogrammica"            "Uraeginthus_bengalus"           
[147] "Amandava_amandava"               "Plectrophenax_nivalis"          
[149] "Serinus_canaria"                 "Serinus_serinus"                
[151] "Loxia_curvirostra"               "Carduelis_carduelis"            
[153] "Carpodacus_roseus"               "Uragus_sibiricus"               
[155] "Pyrrhula_pyrrhula"               "Pinicola_enucleator"            
[157] "Bucanetes_githagineus"           "Coccothraustes_coccothraustes"  
[159] "Mycerobas_affinis"               "Mycerobas_carnipes"             
[161] "Fringilla_montifringilla"        "Fringilla_coelebs"              
[163] "Anas_acuta"                      "Anas_crecca"                    
[165] "Mergus_serrator"                 "Mergus_merganser"               
[167] "Bucephala_clangula"              "Melanitta_nigra"                
[169] "Somateria_mollissima"            "Callonetta_leucophrys"          
[171] "Branta_bernicla"                 "Branta_leucopsis"               
[173] "Anser_anser"                     "Cygnus_columbianus"             
[175] "Tadorna_tadorna"                 "Pucrasia_macrolopha"            
[177] "Phasianus_colchicus"             "Chrysolophus_pictus"            
[179] "Lophura_nycthemera"              "Lophura_ignita"                 
[181] "Syrmaticus_ellioti"              "Syrmaticus_reevesii"            
[183] "Perdix_perdix"                   "Tetrao_urogallus"               
[185] "Lagopus_muta"                    "Lagopus_lagopus"                
[187] "Lophophorus_impejanus"           "Tragopan_temminckii"            
[189] "Pavo_cristatus"                  "Gallus_sonneratii"              
[191] "Rollulus_rouloul"                "Arborophila_torqueola"          

setdiff(dat_organ$phylo, tree$tip.label)      # Database species absent in tree

character(0)

# Exclude mismatched species for consistency
tree_organ <- keep.tip(tree, intersect(tree$tip.label, dat_organ$phylo))
dat_organ <- dat_organ[dat_organ$phylo %in% tree_organ$tip.label, ]

# Re-check for mismatches after pruning
setdiff(tree_organ$tip.label, dat_organ$phylo)

character(0)

setdiff(dat_organ$phylo, tree_organ$tip.label)

character(0)

# Is ultrametric?
is.ultrametric(tree_organ)

[1] TRUE

# how many species?
length(tree_organ$tip.label)

[1] 12

# Compute phylogenetic covariance matrix
A_organ <- ape::vcv.phylo(tree_organ, corr = TRUE)

Model simple

model_simple_liver <- brm(
  log10_organ_size ~ 
    1 + 
    log10_body_size +
    (1 + log10_body_size | sex),
  data = dat_organ,
  family = gaussian(),
    prior = c(
    prior(normal(0.75, 0.5), class = "b", coef = "log10_body_size"),
    prior(normal(0, 2), class = "Intercept"),
    prior(student_t(3, 0, 0.5), class = "sd"),
    prior(student_t(3, 0, 1),   class = "sigma")
  ),
  seed = 6955,
  sample_prior = TRUE, 
  chains = 4, 
  cores = 4, 
  threads = threading(2),
  iter = 4000, 
  warmup = 2000,
  control = list(max_treedepth = 15,
                 adapt_delta = 0.99),
  save_pars = save_pars(all = TRUE),
  silent = TRUE, refresh = 0
)

Running MCMC with 4 parallel chains, with 2 thread(s) per chain...

Chain 2 finished in 2.8 seconds.
Chain 4 finished in 3.5 seconds.
Chain 3 finished in 3.7 seconds.
Chain 1 finished in 4.4 seconds.

All 4 chains finished successfully.
Mean chain execution time: 3.6 seconds.
Total execution time: 4.5 seconds.

Model check

pp_check(model_simple_liver)

Model summary

summary(model_simple_liver)

 Family: gaussian 
  Links: mu = identity; sigma = identity 
Formula: log10_organ_size ~ 1 + log10_body_size + (1 + log10_body_size | sex) 
   Data: dat_organ (Number of observations: 24) 
  Draws: 4 chains, each with iter = 4000; warmup = 2000; thin = 1;
         total post-warmup draws = 8000

Multilevel Hyperparameters:
~sex (Number of levels: 2) 
                               Estimate Est.Error l-95% CI u-95% CI Rhat
sd(Intercept)                      0.30      0.31     0.01     1.12 1.00
sd(log10_body_size)                0.18      0.22     0.00     0.81 1.00
cor(Intercept,log10_body_size)    -0.08      0.59    -0.97     0.95 1.00
                               Bulk_ESS Tail_ESS
sd(Intercept)                      2690     2972
sd(log10_body_size)                1903     3263
cor(Intercept,log10_body_size)     4124     4348

Regression Coefficients:
                Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept          -1.34      0.31    -1.98    -0.75 1.00     2946     2317
log10_body_size     0.85      0.15     0.48     1.14 1.00     1706     1586

Further Distributional Parameters:
      Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma     0.18      0.03     0.13     0.26 1.00     5259     4010

Draws were sampled using sample(hmc). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).

I will next extract, for each sex, the estimated slope and intercept, together with the 95% credible intervals.

# Extract combined coefficients (fixed + random)
coef(model_simple_liver)$sex %>%
{tibble(
  sex = dimnames(.)[[1]],
  intercept    = .[, "Estimate", "Intercept"],
  intercept_low  = .[, "Q2.5", "Intercept"], 
  intercept_high = .[, "Q97.5", "Intercept"]
)} %>%
bind_cols(
  tibble(
    sex = dimnames(coef(model_simple_liver)$sex)[[1]],
    slope = coef(model_simple_liver)$sex[, "Estimate", "log10_body_size"]
  ) %>% select(slope),
  tibble(
    sex = dimnames(coef(model_simple_liver)$sex)[[1]],
    slope_low  = coef(model_simple_liver)$sex[, "Q2.5", "log10_body_size"],
    slope_high = coef(model_simple_liver)$sex[, "Q97.5", "log10_body_size"]
  ) %>% select(slope_low, slope_high)
)

# A tibble: 2 × 7
  sex    intercept intercept_low intercept_high slope slope_low slope_high
  <chr>      <dbl>         <dbl>          <dbl> <dbl>     <dbl>      <dbl>
1 female     -1.29         -1.56          -1.01 0.868     0.756      0.976
2 male       -1.36         -1.63          -1.10 0.876     0.772      0.986

Model with phylogeny

model_phylo_liver <- brm(
  log10_organ_size ~ 
    1 + 
    log10_body_size +
    (1 + log10_body_size | sex) +
    (1 | gr(phylo, cov = A_organ)),
  data = dat_organ,
  data2 = list(A_organ = A_organ),
  family = gaussian(),
    prior = c(
    prior(normal(0.75, 0.5), class = "b", coef = "log10_body_size"),
    prior(normal(0, 2), class = "Intercept"),
    prior(student_t(3, 0, 0.5), class = "sd"),
    prior(student_t(3, 0, 1),   class = "sigma")
  ),
  seed = 6955,
  sample_prior = TRUE, 
  chains = 4, 
  cores = 4, 
  threads = threading(2),
  iter = 4000, 
  warmup = 2000,
  control = list(max_treedepth = 15,
                 adapt_delta = 0.99),
  save_pars = save_pars(all = TRUE),
  silent = TRUE, refresh = 0
)

Running MCMC with 4 parallel chains, with 2 thread(s) per chain...

Chain 3 finished in 12.6 seconds.
Chain 2 finished in 12.7 seconds.
Chain 1 finished in 12.9 seconds.
Chain 4 finished in 16.0 seconds.

All 4 chains finished successfully.
Mean chain execution time: 13.5 seconds.
Total execution time: 16.1 seconds.

Model check

pp_check(model_phylo_liver)

Model summary

summary(model_phylo_liver)

 Family: gaussian 
  Links: mu = identity; sigma = identity 
Formula: log10_organ_size ~ 1 + log10_body_size + (1 + log10_body_size | sex) + (1 | gr(phylo, cov = A_organ)) 
   Data: dat_organ (Number of observations: 24) 
  Draws: 4 chains, each with iter = 4000; warmup = 2000; thin = 1;
         total post-warmup draws = 8000

Multilevel Hyperparameters:
~phylo (Number of levels: 12) 
              Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept)     0.18      0.06     0.10     0.32 1.00     2911     4442

~sex (Number of levels: 2) 
                               Estimate Est.Error l-95% CI u-95% CI Rhat
sd(Intercept)                      0.25      0.28     0.01     1.00 1.00
sd(log10_body_size)                0.15      0.19     0.00     0.68 1.00
cor(Intercept,log10_body_size)    -0.04      0.61    -0.97     0.96 1.00
                               Bulk_ESS Tail_ESS
sd(Intercept)                      3265     3752
sd(log10_body_size)                2489     4785
cor(Intercept,log10_body_size)     5417     5026

Regression Coefficients:
                Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept          -1.48      0.27    -2.06    -0.97 1.00     3578     4630
log10_body_size     0.88      0.12     0.58     1.12 1.00     2828     2704

Further Distributional Parameters:
      Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma     0.07      0.01     0.04     0.10 1.00     3796     4733

Draws were sampled using sample(hmc). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).

Phylogenetic signal

hyp <- paste(
  "sd_phylo__Intercept^2 /",
  "(sd_phylo__Intercept^2 + sd_sex__Intercept^2 + sigma^2) = 0"
)
(hyp <- hypothesis(model_phylo_liver, hyp, class = NULL))

Hypothesis Tests for class :
                Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
1 (sd_phylo__Interc... = 0     0.48       0.3     0.02     0.94        0.2
  Post.Prob Star
1      0.17    *
---
'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
'*': For one-sided hypotheses, the posterior probability exceeds 95%;
for two-sided hypotheses, the value tested against lies outside the 95%-CI.
Posterior probabilities of point hypotheses assume equal prior probabilities.

lambda_liver <- hyp$hypothesis$Estimate

I will next extract, for each sex, the estimated slope and intercept, together with the 95% credible intervals.

# Extract combined coefficients (fixed + random)
coef(model_phylo_liver)$sex %>%
{tibble(
  sex = dimnames(.)[[1]],
  intercept    = .[, "Estimate", "Intercept"],
  intercept_low  = .[, "Q2.5", "Intercept"], 
  intercept_high = .[, "Q97.5", "Intercept"]
)} %>%
bind_cols(
  tibble(
    sex = dimnames(coef(model_phylo_liver)$sex)[[1]],
    slope = coef(model_phylo_liver)$sex[, "Estimate", "log10_body_size"]
  ) %>% select(slope),
  tibble(
    sex = dimnames(coef(model_phylo_liver)$sex)[[1]],
    slope_low  = coef(model_phylo_liver)$sex[, "Q2.5", "log10_body_size"],
    slope_high = coef(model_phylo_liver)$sex[, "Q97.5", "log10_body_size"]
  ) %>% select(slope_low, slope_high)
)

# A tibble: 2 × 7
  sex    intercept intercept_low intercept_high slope slope_low slope_high
  <chr>      <dbl>         <dbl>          <dbl> <dbl>     <dbl>      <dbl>
1 female     -1.45         -1.73          -1.18 0.897     0.827      0.971
2 male       -1.50         -1.77          -1.24 0.894     0.825      0.968

Model comparison

loo_simple <- loo(model_simple_liver)
loo_phylo <- loo(model_phylo_liver)
loo_compare(loo_simple, loo_phylo)

                   elpd_diff se_diff
model_phylo_liver    0.0       0.0  
model_simple_liver -19.6       3.8  

In this comparison, the model that accounts for phylogeny performs better to the model that treats species as independent observational units. The phylogenetic model (model_phylo_liver) is used as the reference with elpd_diff = 0, whereas the simpler model (model_simple_liver) has an expected log predictive density (ELPD) that is about 19.6 units lower, with an associated standard error of 3.8. In the context of leave‑one‑out cross‑validation, differences exceeding roughly four to five times their standard error are typically regarded as strong evidence (Vehtari et al., 2016; Sivula et al., 2025). Here, 19.6/3.8≈5.2, which provides strong evidence in favour of the phylogenetic model.

Heart

Filter data and prune tree

# Filter organ of interest
dat_organ <- dat_mean %>%
  group_by(organ_grouped, sex) %>%
  ungroup() %>%
  filter(organ_grouped == "heart")

# Check for database/tree species mismatches
setdiff(tree$tip.label, dat_organ$phylo)      # Tree species absent in database

  [1] "Petrochromis_famula"             "Lobochilotes_labiatus"          
  [3] "Simochromis_diagramma"           "Petrochromis_orthognathus"      
  [5] "Ctenochromis_horei"              "Limnotilapia_dardennii"         
  [7] "Gnathochromis_pfefferi"          "Tropheus_moorii"                
  [9] "Tropheus_brichardi"              "Haplotaxodon_microlepis"        
 [11] "Perissodus_microlepis"           "Benthochromis_tricoti"          
 [13] "Cyprichromis_leptosoma"          "Greenwoodochromis_christyi"     
 [15] "Limnochromis_staneri"            "Gnathochromis_permaxillaris"    
 [17] "Baileychromis_centropomoides"    "Triglachromis_otostigma"        
 [19] "Cyphotilapia_frontosa"           "Ophthalmotilapia_ventralis"     
 [21] "Cyathopharynx_furcifer"          "Ophthalmotilapia_nasuta"        
 [23] "Ophthalmotilapia_boops"          "Aulonocranus_dewindti"          
 [25] "Ectodus_descampsii"              "Callochromis_melanostigma"      
 [27] "Xenotilapia_melanogenys"         "Xenotilapia_flavipinnis"        
 [29] "Eretmodus_cyanostictus"          "Tanganicodus_irsacae"           
 [31] "Spathodus_marlieri"              "Spathodus_erythrodon"           
 [33] "Neolamprologus_brichardi"        "Julidochromis_regani"           
 [35] "Julidochromis_marlieri"          "Neolamprologus_tetracanthus"    
 [37] "Telmatochromis_temporalis"       "Lepidiolamprologus_elongatus"   
 [39] "Lepidiolamprologus_profundicola" "Lepidiolamprologus_nkambae"     
 [41] "Altolamprologus_compressiceps"   "Neolamprologus_brevis"          
 [43] "Chalinochromis_brichardi"        "Julidochromis_ornatus"          
 [45] "Lamprologus_ornatipinnis"        "Neolamprologus_pulcher"         
 [47] "Variabilichromis_moorii"         "Neolamprologus_tretocephalus"   
 [49] "Neolamprologus_sexfasciatus"     "Trematocara_unimaculatum"       
 [51] "Hemibates_stenosoma"             "Bathybates_ferox"               
 [53] "Oreochromis_niloticus"           "Nerophis_lumbriciformis"        
 [55] "Syngnathus_abaster"              "Syngnathus_schlegeli"           
 [57] "Hippocampus_comes"               "Hippocampus_trimaculatus"       
 [59] "Hippocampus_kuda"                "Hippocampus_spinosissimus"      
 [61] "Hippocampus_abdominalis"         "Hippichthys_cyanospilos"        
 [63] "Syngnathoides_biaculeatus"       "Corythoichthys_intestinalis"    
 [65] "Corythoichthys_haematopterus"    "Doryichthys_boaja"              
 [67] "Doryrhamphus_japonicus"          "Entelurus_aequoreus"            
 [69] "Anguilla_anguilla"               "Syncerus_caffer"                
 [71] "Tragelaphus_eurycerus"           "Tragelaphus_scriptus"           
 [73] "Redunca_arundinum"               "Antidorcas_marsupialis"         
 [75] "Nanger_granti"                   "Raphicerus_campestris"          
 [77] "Cephalophus_natalensis"          "Sylvicapra_grimmia"             
 [79] "Oreotragus_oreotragus"           "Hippotragus_equinus"            
 [81] "Addax_nasomaculatus"             "Oryx_gazella"                   
 [83] "Connochaetes_taurinus"           "Damaliscus_lunatus"             
 [85] "Ovis_aries"                      "Aepyceros_melampus"             
 [87] "Pteropus_alecto"                 "Pteropus_poliocephalus"         
 [89] "Pteropus_scapulatus"             "Chlorocebus_aethiops"           
 [91] "Chlorocebus_sabaeus"             "Erythrocebus_patas"             
 [93] "Papio_cynocephalus"              "Papio_anubis"                   
 [95] "Cercocebus_atys"                 "Macaca_arctoides"               
 [97] "Macaca_mulatta"                  "Macaca_maura"                   
 [99] "Trachypithecus_francoisi"        "Platycercus_caledonicus"        
[101] "Platycercus_elegans"             "Platycercus_eximius"            
[103] "Platycercus_venustus"            "Barnardius_zonarius"            
[105] "Northiella_haematogaster"        "Lathamus_discolor"              
[107] "Neophema_chrysostoma"            "Neophema_pulchella"             
[109] "Psittacula_krameri"              "Eclectus_roratus"               
[111] "Aprosmictus_jonquillaceus"       "Alisterus_scapularis"           
[113] "Alisterus_amboinensis"           "Polytelis_alexandrae"           
[115] "Trichoglossus_haematodus"        "Agapornis_lilianae"             
[117] "Agapornis_taranta"               "Loriculus_vernalis"             
[119] "Ara_ararauna"                    "Guaruba_guarouba"               
[121] "Enicognathus_leptorhynchus"      "Pionites_melanocephalus"        
[123] "Forpus_coelestis"                "Forpus_passerinus"              
[125] "Amazona_leucocephala"            "Amazona_albifrons"              
[127] "Amazona_pretrei"                 "Amazona_vinacea"                
[129] "Amazona_finschi"                 "Amazona_amazonica"              
[131] "Amazona_ochrocephala"            "Amazona_aestiva"                
[133] "Brotogeris_versicolurus"         "Brotogeris_pyrrhoptera"         
[135] "Bolborhynchus_lineola"           "Poicephalus_gulielmi"           
[137] "Poicephalus_meyeri"              "Psittacus_erithacus"            
[139] "Serinus_mennelli"                "Ficedula_hypoleuca"             
[141] "Padda_oryzivora"                 "Lonchura_punctulata"            
[143] "Lonchura_flaviprymna"            "Lonchura_bicolor"               
[145] "Hypargos_niveoguttatus"          "Pytilia_hypogrammica"           
[147] "Uraeginthus_bengalus"            "Amandava_amandava"              
[149] "Plectrophenax_nivalis"           "Serinus_canaria"                
[151] "Serinus_serinus"                 "Loxia_curvirostra"              
[153] "Carduelis_carduelis"             "Carpodacus_roseus"              
[155] "Uragus_sibiricus"                "Pyrrhula_pyrrhula"              
[157] "Pinicola_enucleator"             "Bucanetes_githagineus"          
[159] "Coccothraustes_coccothraustes"   "Mycerobas_affinis"              
[161] "Mycerobas_carnipes"              "Fringilla_montifringilla"       
[163] "Fringilla_coelebs"               "Anas_acuta"                     
[165] "Anas_crecca"                     "Mergus_serrator"                
[167] "Mergus_merganser"                "Bucephala_clangula"             
[169] "Melanitta_nigra"                 "Somateria_mollissima"           
[171] "Callonetta_leucophrys"           "Branta_bernicla"                
[173] "Branta_leucopsis"                "Anser_anser"                    
[175] "Cygnus_columbianus"              "Tadorna_tadorna"                
[177] "Pucrasia_macrolopha"             "Phasianus_colchicus"            
[179] "Chrysolophus_pictus"             "Lophura_nycthemera"             
[181] "Lophura_ignita"                  "Syrmaticus_ellioti"             
[183] "Syrmaticus_reevesii"             "Perdix_perdix"                  
[185] "Tetrao_urogallus"                "Lagopus_muta"                   
[187] "Lagopus_lagopus"                 "Lophophorus_impejanus"          
[189] "Tragopan_temminckii"             "Pavo_cristatus"                 
[191] "Gallus_gallus"                   "Gallus_sonneratii"              
[193] "Rollulus_rouloul"                "Arborophila_torqueola"          

setdiff(dat_organ$phylo, tree$tip.label)      # Database species absent in tree

character(0)

# Exclude mismatched species for consistency
tree_organ <- keep.tip(tree, intersect(tree$tip.label, dat_organ$phylo))
dat_organ <- dat_organ[dat_organ$phylo %in% tree_organ$tip.label, ]

# Re-check for mismatches after pruning
setdiff(tree_organ$tip.label, dat_organ$phylo)

character(0)

setdiff(dat_organ$phylo, tree_organ$tip.label)

character(0)

# Is ultrametric?
is.ultrametric(tree_organ)

[1] TRUE

# how many species?
length(tree_organ$tip.label)

[1] 10

# Compute phylogenetic covariance matrix
A_organ <- ape::vcv.phylo(tree_organ, corr = TRUE)

Model simple

model_simple_heart <- brm(
  log10_organ_size ~ 
    1 + 
    log10_body_size +
    (1 + log10_body_size | sex),
  data = dat_organ,
  family = gaussian(),
    prior = c(
    prior(normal(0.75, 0.5), class = "b", coef = "log10_body_size"),
    prior(normal(0, 2), class = "Intercept"),
    prior(student_t(3, 0, 0.5), class = "sd"),
    prior(student_t(3, 0, 1),   class = "sigma")
  ),
  seed = 6955,
  sample_prior = TRUE, 
  chains = 4, 
  cores = 4, 
  threads = threading(2),
  iter = 4000, 
  warmup = 2000,
  control = list(max_treedepth = 15,
                 adapt_delta = 0.99),
  save_pars = save_pars(all = TRUE),
  silent = TRUE, refresh = 0
)

Running MCMC with 4 parallel chains, with 2 thread(s) per chain...

Chain 2 finished in 2.1 seconds.
Chain 4 finished in 2.6 seconds.
Chain 1 finished in 3.2 seconds.
Chain 3 finished in 3.1 seconds.

All 4 chains finished successfully.
Mean chain execution time: 2.8 seconds.
Total execution time: 3.3 seconds.

Model check

pp_check(model_simple_heart)

Model summary

summary(model_simple_heart)

 Family: gaussian 
  Links: mu = identity; sigma = identity 
Formula: log10_organ_size ~ 1 + log10_body_size + (1 + log10_body_size | sex) 
   Data: dat_organ (Number of observations: 20) 
  Draws: 4 chains, each with iter = 4000; warmup = 2000; thin = 1;
         total post-warmup draws = 8000

Multilevel Hyperparameters:
~sex (Number of levels: 2) 
                               Estimate Est.Error l-95% CI u-95% CI Rhat
sd(Intercept)                      0.27      0.30     0.01     1.04 1.00
sd(log10_body_size)                0.19      0.22     0.00     0.80 1.00
cor(Intercept,log10_body_size)    -0.07      0.61    -0.97     0.95 1.00
                               Bulk_ESS Tail_ESS
sd(Intercept)                      3635     3605
sd(log10_body_size)                2149     3479
cor(Intercept,log10_body_size)     4205     4565

Regression Coefficients:
                Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept          -2.92      0.29    -3.49    -2.35 1.00     3737     3845
log10_body_size     1.20      0.16     0.79     1.49 1.00     2413     2315

Further Distributional Parameters:
      Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma     0.25      0.05     0.18     0.36 1.00     5488     3595

Draws were sampled using sample(hmc). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).

I will next extract, for each sex, the estimated slope and intercept, together with the 95% credible intervals.

# Extract combined coefficients (fixed + random)
coef(model_simple_heart)$sex %>%
{tibble(
  sex = dimnames(.)[[1]],
  intercept    = .[, "Estimate", "Intercept"],
  intercept_low  = .[, "Q2.5", "Intercept"], 
  intercept_high = .[, "Q97.5", "Intercept"]
)} %>%
bind_cols(
  tibble(
    sex = dimnames(coef(model_simple_heart)$sex)[[1]],
    slope = coef(model_simple_heart)$sex[, "Estimate", "log10_body_size"]
  ) %>% select(slope),
  tibble(
    sex = dimnames(coef(model_simple_heart)$sex)[[1]],
    slope_low  = coef(model_simple_heart)$sex[, "Q2.5", "log10_body_size"],
    slope_high = coef(model_simple_heart)$sex[, "Q97.5", "log10_body_size"]
  ) %>% select(slope_low, slope_high)
)

# A tibble: 2 × 7
  sex    intercept intercept_low intercept_high slope slope_low slope_high
  <chr>      <dbl>         <dbl>          <dbl> <dbl>     <dbl>      <dbl>
1 female     -2.94         -3.21          -2.67  1.24      1.13       1.35
2 male       -2.91         -3.16          -2.65  1.23      1.13       1.34

Model with phylogeny

model_phylo_heart <- brm(
  log10_organ_size ~ 
    1 + 
    log10_body_size +
    (1 + log10_body_size | sex) +
    (1 | gr(phylo, cov = A_organ)),
  data = dat_organ,
  data2 = list(A_organ = A_organ),
  family = gaussian(),
    prior = c(
    prior(normal(0.75, 0.5), class = "b", coef = "log10_body_size"),
    prior(normal(0, 2), class = "Intercept"),
    prior(student_t(3, 0, 0.5), class = "sd"),
    prior(student_t(3, 0, 1),   class = "sigma")
  ),
  seed = 6955,
  sample_prior = TRUE, 
  chains = 4, 
  cores = 4, 
  threads = threading(2),
  iter = 4000, 
  warmup = 2000,
  control = list(max_treedepth = 15,
                 adapt_delta = 0.99),
  save_pars = save_pars(all = TRUE),
  silent = TRUE, refresh = 0
)

Running MCMC with 4 parallel chains, with 2 thread(s) per chain...

Chain 4 finished in 13.3 seconds.
Chain 3 finished in 14.4 seconds.
Chain 1 finished in 14.5 seconds.
Chain 2 finished in 15.3 seconds.

All 4 chains finished successfully.
Mean chain execution time: 14.4 seconds.
Total execution time: 15.4 seconds.

Model check

pp_check(model_phylo_heart)

Model summary

summary(model_phylo_heart)

 Family: gaussian 
  Links: mu = identity; sigma = identity 
Formula: log10_organ_size ~ 1 + log10_body_size + (1 + log10_body_size | sex) + (1 | gr(phylo, cov = A_organ)) 
   Data: dat_organ (Number of observations: 20) 
  Draws: 4 chains, each with iter = 4000; warmup = 2000; thin = 1;
         total post-warmup draws = 8000

Multilevel Hyperparameters:
~phylo (Number of levels: 10) 
              Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept)     0.53      0.15     0.31     0.90 1.00     1983     2846

~sex (Number of levels: 2) 
                               Estimate Est.Error l-95% CI u-95% CI Rhat
sd(Intercept)                      0.19      0.25     0.00     0.90 1.00
sd(log10_body_size)                0.14      0.19     0.00     0.68 1.00
cor(Intercept,log10_body_size)    -0.05      0.62    -0.98     0.97 1.00
                               Bulk_ESS Tail_ESS
sd(Intercept)                      2944     3477
sd(log10_body_size)                1979     2037
cor(Intercept,log10_body_size)     4467     2200

Regression Coefficients:
                Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept          -2.63      0.39    -3.38    -1.83 1.00     2352     3851
log10_body_size     0.95      0.14     0.65     1.24 1.00     1652     1970

Further Distributional Parameters:
      Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma     0.05      0.02     0.03     0.10 1.00     1526     1969

Draws were sampled using sample(hmc). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).

Phylogenetic signal

hyp <- paste(
  "sd_phylo__Intercept^2 /",
  "(sd_phylo__Intercept^2 + sd_sex__Intercept^2 + sigma^2) = 0"
)
(hyp <- hypothesis(model_phylo_heart, hyp, class = NULL))

Hypothesis Tests for class :
                Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
1 (sd_phylo__Interc... = 0     0.84      0.21     0.22        1          0
  Post.Prob Star
1         0    *
---
'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
'*': For one-sided hypotheses, the posterior probability exceeds 95%;
for two-sided hypotheses, the value tested against lies outside the 95%-CI.
Posterior probabilities of point hypotheses assume equal prior probabilities.

lambda_heart <- hyp$hypothesis$Estimate

I will next extract, for each sex, the estimated slope and intercept, together with the 95% credible intervals.

# Extract combined coefficients (fixed + random)
coef(model_phylo_heart)$sex %>%
{tibble(
  sex = dimnames(.)[[1]],
  intercept    = .[, "Estimate", "Intercept"],
  intercept_low  = .[, "Q2.5", "Intercept"], 
  intercept_high = .[, "Q97.5", "Intercept"]
)} %>%
bind_cols(
  tibble(
    sex = dimnames(coef(model_phylo_heart)$sex)[[1]],
    slope = coef(model_phylo_heart)$sex[, "Estimate", "log10_body_size"]
  ) %>% select(slope),
  tibble(
    sex = dimnames(coef(model_phylo_heart)$sex)[[1]],
    slope_low  = coef(model_phylo_heart)$sex[, "Q2.5", "log10_body_size"],
    slope_high = coef(model_phylo_heart)$sex[, "Q97.5", "log10_body_size"]
  ) %>% select(slope_low, slope_high)
)

# A tibble: 2 × 7
  sex    intercept intercept_low intercept_high slope slope_low slope_high
  <chr>      <dbl>         <dbl>          <dbl> <dbl>     <dbl>      <dbl>
1 female     -2.64         -3.27          -1.95 0.951     0.767       1.12
2 male       -2.63         -3.26          -1.94 0.957     0.786       1.12

Model comparison

loo_simple <- loo(model_simple_heart, moment_match = TRUE)

Running /Library/Frameworks/R.framework/Resources/bin/R CMD SHLIB foo.c
using C compiler: ‘Apple clang version 17.0.0 (clang-1700.6.3.2)’
using SDK: ‘MacOSX26.2.sdk’
clang -arch arm64 -I"/Library/Frameworks/R.framework/Resources/include" -DNDEBUG   -I"/Library/Frameworks/R.framework/Versions/4.3-arm64/Resources/library/Rcpp/include/"  -I"/Library/Frameworks/R.framework/Versions/4.3-arm64/Resources/library/RcppEigen/include/"  -I"/Library/Frameworks/R.framework/Versions/4.3-arm64/Resources/library/RcppEigen/include/unsupported"  -I"/Library/Frameworks/R.framework/Versions/4.3-arm64/Resources/library/BH/include" -I"/Library/Frameworks/R.framework/Versions/4.3-arm64/Resources/library/StanHeaders/include/src/"  -I"/Library/Frameworks/R.framework/Versions/4.3-arm64/Resources/library/StanHeaders/include/"  -I"/Library/Frameworks/R.framework/Versions/4.3-arm64/Resources/library/RcppParallel/include/"  -I"/Library/Frameworks/R.framework/Versions/4.3-arm64/Resources/library/rstan/include" -DEIGEN_NO_DEBUG  -DBOOST_DISABLE_ASSERTS  -DBOOST_PENDING_INTEGER_LOG2_HPP  -DSTAN_THREADS  -DUSE_STANC3 -DSTRICT_R_HEADERS  -DBOOST_PHOENIX_NO_VARIADIC_EXPRESSION  -D_HAS_AUTO_PTR_ETC=0  -include '/Library/Frameworks/R.framework/Versions/4.3-arm64/Resources/library/StanHeaders/include/stan/math/prim/fun/Eigen.hpp'  -D_REENTRANT -DRCPP_PARALLEL_USE_TBB=1   -I/opt/R/arm64/include    -fPIC  -falign-functions=64 -Wall -g -O2  -c foo.c -o foo.o
In file included from <built-in>:1:
In file included from /Library/Frameworks/R.framework/Versions/4.3-arm64/Resources/library/StanHeaders/include/stan/math/prim/fun/Eigen.hpp:22:
In file included from /Library/Frameworks/R.framework/Versions/4.3-arm64/Resources/library/RcppEigen/include/Eigen/Dense:1:
In file included from /Library/Frameworks/R.framework/Versions/4.3-arm64/Resources/library/RcppEigen/include/Eigen/Core:19:
/Library/Frameworks/R.framework/Versions/4.3-arm64/Resources/library/RcppEigen/include/Eigen/src/Core/util/Macros.h:679:10: fatal error: 'cmath' file not found
  679 | #include <cmath>
      |          ^~~~~~~
1 error generated.
make: *** [foo.o] Error 1

loo_phylo <- loo(model_phylo_heart, moment_match = TRUE)

Running /Library/Frameworks/R.framework/Resources/bin/R CMD SHLIB foo.c
using C compiler: ‘Apple clang version 17.0.0 (clang-1700.6.3.2)’
using SDK: ‘MacOSX26.2.sdk’
clang -arch arm64 -I"/Library/Frameworks/R.framework/Resources/include" -DNDEBUG   -I"/Library/Frameworks/R.framework/Versions/4.3-arm64/Resources/library/Rcpp/include/"  -I"/Library/Frameworks/R.framework/Versions/4.3-arm64/Resources/library/RcppEigen/include/"  -I"/Library/Frameworks/R.framework/Versions/4.3-arm64/Resources/library/RcppEigen/include/unsupported"  -I"/Library/Frameworks/R.framework/Versions/4.3-arm64/Resources/library/BH/include" -I"/Library/Frameworks/R.framework/Versions/4.3-arm64/Resources/library/StanHeaders/include/src/"  -I"/Library/Frameworks/R.framework/Versions/4.3-arm64/Resources/library/StanHeaders/include/"  -I"/Library/Frameworks/R.framework/Versions/4.3-arm64/Resources/library/RcppParallel/include/"  -I"/Library/Frameworks/R.framework/Versions/4.3-arm64/Resources/library/rstan/include" -DEIGEN_NO_DEBUG  -DBOOST_DISABLE_ASSERTS  -DBOOST_PENDING_INTEGER_LOG2_HPP  -DSTAN_THREADS  -DUSE_STANC3 -DSTRICT_R_HEADERS  -DBOOST_PHOENIX_NO_VARIADIC_EXPRESSION  -D_HAS_AUTO_PTR_ETC=0  -include '/Library/Frameworks/R.framework/Versions/4.3-arm64/Resources/library/StanHeaders/include/stan/math/prim/fun/Eigen.hpp'  -D_REENTRANT -DRCPP_PARALLEL_USE_TBB=1   -I/opt/R/arm64/include    -fPIC  -falign-functions=64 -Wall -g -O2  -c foo.c -o foo.o
In file included from <built-in>:1:
In file included from /Library/Frameworks/R.framework/Versions/4.3-arm64/Resources/library/StanHeaders/include/stan/math/prim/fun/Eigen.hpp:22:
In file included from /Library/Frameworks/R.framework/Versions/4.3-arm64/Resources/library/RcppEigen/include/Eigen/Dense:1:
In file included from /Library/Frameworks/R.framework/Versions/4.3-arm64/Resources/library/RcppEigen/include/Eigen/Core:19:
/Library/Frameworks/R.framework/Versions/4.3-arm64/Resources/library/RcppEigen/include/Eigen/src/Core/util/Macros.h:679:10: fatal error: 'cmath' file not found
  679 | #include <cmath>
      |          ^~~~~~~
1 error generated.
make: *** [foo.o] Error 1

loo_compare(loo_simple, loo_phylo)

                   elpd_diff se_diff
model_phylo_heart    0.0       0.0  
model_simple_heart -25.1       3.5  

In this comparison, the model that accounts for phylogeny is clearly preferable to the model that treats species as independent observational units. The phylogenetic model (model_phylo_heart) is used as the reference with elpd_diff = 0, whereas the simpler model (model_simple_heart) has an expected log predictive density (ELPD) that is about 25.1 units lower, with an associated standard error of 3.5. In the context of leave‑one‑out cross‑validation, differences exceeding roughly four times their standard error are typically regarded as strong evidence. Here, 25.1/3.5≈7.2, indicating a very large difference relative to its uncertainty, and thus providing strong support for the phylogenetic model.

Pituitary glands

Filter data and prune tree

# Filter organ of interest
dat_organ <- dat_mean %>%
  group_by(organ_grouped, sex) %>%
  ungroup() %>%
  filter(organ_grouped == "pituitary glands")

# Check for database/tree species mismatches
setdiff(tree$tip.label, dat_organ$phylo)      # Tree species absent in database

  [1] "Petrochromis_famula"             "Lobochilotes_labiatus"          
  [3] "Simochromis_diagramma"           "Petrochromis_orthognathus"      
  [5] "Ctenochromis_horei"              "Limnotilapia_dardennii"         
  [7] "Gnathochromis_pfefferi"          "Tropheus_moorii"                
  [9] "Tropheus_brichardi"              "Haplotaxodon_microlepis"        
 [11] "Perissodus_microlepis"           "Benthochromis_tricoti"          
 [13] "Cyprichromis_leptosoma"          "Greenwoodochromis_christyi"     
 [15] "Limnochromis_staneri"            "Gnathochromis_permaxillaris"    
 [17] "Baileychromis_centropomoides"    "Triglachromis_otostigma"        
 [19] "Cyphotilapia_frontosa"           "Ophthalmotilapia_ventralis"     
 [21] "Cyathopharynx_furcifer"          "Ophthalmotilapia_nasuta"        
 [23] "Ophthalmotilapia_boops"          "Aulonocranus_dewindti"          
 [25] "Ectodus_descampsii"              "Callochromis_melanostigma"      
 [27] "Xenotilapia_melanogenys"         "Xenotilapia_flavipinnis"        
 [29] "Eretmodus_cyanostictus"          "Tanganicodus_irsacae"           
 [31] "Spathodus_marlieri"              "Spathodus_erythrodon"           
 [33] "Neolamprologus_brichardi"        "Julidochromis_regani"           
 [35] "Julidochromis_marlieri"          "Neolamprologus_tetracanthus"    
 [37] "Telmatochromis_temporalis"       "Lepidiolamprologus_elongatus"   
 [39] "Lepidiolamprologus_profundicola" "Lepidiolamprologus_nkambae"     
 [41] "Altolamprologus_compressiceps"   "Neolamprologus_brevis"          
 [43] "Chalinochromis_brichardi"        "Julidochromis_ornatus"          
 [45] "Lamprologus_ornatipinnis"        "Neolamprologus_pulcher"         
 [47] "Variabilichromis_moorii"         "Neolamprologus_tretocephalus"   
 [49] "Neolamprologus_sexfasciatus"     "Trematocara_unimaculatum"       
 [51] "Hemibates_stenosoma"             "Bathybates_ferox"               
 [53] "Oreochromis_niloticus"           "Poecilia_reticulata"            
 [55] "Nerophis_lumbriciformis"         "Syngnathus_abaster"             
 [57] "Syngnathus_schlegeli"            "Hippocampus_comes"              
 [59] "Hippocampus_trimaculatus"        "Hippocampus_kuda"               
 [61] "Hippocampus_spinosissimus"       "Hippocampus_abdominalis"        
 [63] "Hippichthys_cyanospilos"         "Syngnathoides_biaculeatus"      
 [65] "Corythoichthys_intestinalis"     "Corythoichthys_haematopterus"   
 [67] "Doryichthys_boaja"               "Doryrhamphus_japonicus"         
 [69] "Entelurus_aequoreus"             "Anguilla_anguilla"              
 [71] "Syncerus_caffer"                 "Tragelaphus_eurycerus"          
 [73] "Tragelaphus_scriptus"            "Redunca_arundinum"              
 [75] "Antidorcas_marsupialis"          "Nanger_granti"                  
 [77] "Raphicerus_campestris"           "Cephalophus_natalensis"         
 [79] "Sylvicapra_grimmia"              "Oreotragus_oreotragus"          
 [81] "Hippotragus_equinus"             "Addax_nasomaculatus"            
 [83] "Oryx_gazella"                    "Connochaetes_taurinus"          
 [85] "Damaliscus_lunatus"              "Ovis_aries"                     
 [87] "Aepyceros_melampus"              "Lasiopodomys_brandtii"          
 [89] "Mus_musculus"                    "Meriones_unguiculatus"          
 [91] "Chlorocebus_aethiops"            "Chlorocebus_sabaeus"            
 [93] "Erythrocebus_patas"              "Papio_cynocephalus"             
 [95] "Papio_anubis"                    "Cercocebus_atys"                
 [97] "Macaca_arctoides"                "Macaca_mulatta"                 
 [99] "Macaca_maura"                    "Trachypithecus_francoisi"       
[101] "Phrynocephalus_vlangalii"        "Platycercus_caledonicus"        
[103] "Platycercus_elegans"             "Platycercus_eximius"            
[105] "Platycercus_venustus"            "Barnardius_zonarius"            
[107] "Northiella_haematogaster"        "Lathamus_discolor"              
[109] "Neophema_chrysostoma"            "Neophema_pulchella"             
[111] "Psittacula_krameri"              "Eclectus_roratus"               
[113] "Aprosmictus_jonquillaceus"       "Alisterus_scapularis"           
[115] "Alisterus_amboinensis"           "Polytelis_alexandrae"           
[117] "Trichoglossus_haematodus"        "Agapornis_lilianae"             
[119] "Agapornis_taranta"               "Loriculus_vernalis"             
[121] "Ara_ararauna"                    "Guaruba_guarouba"               
[123] "Enicognathus_leptorhynchus"      "Pionites_melanocephalus"        
[125] "Forpus_coelestis"                "Forpus_passerinus"              
[127] "Amazona_leucocephala"            "Amazona_albifrons"              
[129] "Amazona_pretrei"                 "Amazona_vinacea"                
[131] "Amazona_finschi"                 "Amazona_amazonica"              
[133] "Amazona_ochrocephala"            "Amazona_aestiva"                
[135] "Brotogeris_versicolurus"         "Brotogeris_pyrrhoptera"         
[137] "Bolborhynchus_lineola"           "Poicephalus_gulielmi"           
[139] "Poicephalus_meyeri"              "Psittacus_erithacus"            
[141] "Serinus_mennelli"                "Ficedula_hypoleuca"             
[143] "Padda_oryzivora"                 "Lonchura_punctulata"            
[145] "Lonchura_flaviprymna"            "Lonchura_bicolor"               
[147] "Hypargos_niveoguttatus"          "Pytilia_hypogrammica"           
[149] "Uraeginthus_bengalus"            "Amandava_amandava"              
[151] "Plectrophenax_nivalis"           "Serinus_canaria"                
[153] "Serinus_serinus"                 "Loxia_curvirostra"              
[155] "Carduelis_carduelis"             "Carpodacus_roseus"              
[157] "Uragus_sibiricus"                "Pyrrhula_pyrrhula"              
[159] "Pinicola_enucleator"             "Bucanetes_githagineus"          
[161] "Coccothraustes_coccothraustes"   "Mycerobas_affinis"              
[163] "Mycerobas_carnipes"              "Fringilla_montifringilla"       
[165] "Fringilla_coelebs"               "Anas_platyrhynchos"             
[167] "Anas_acuta"                      "Anas_crecca"                    
[169] "Mergus_serrator"                 "Mergus_merganser"               
[171] "Bucephala_clangula"              "Melanitta_nigra"                
[173] "Somateria_mollissima"            "Callonetta_leucophrys"          
[175] "Branta_bernicla"                 "Branta_leucopsis"               
[177] "Anser_anser"                     "Cygnus_columbianus"             
[179] "Tadorna_tadorna"                 "Coturnix_japonica"              
[181] "Pucrasia_macrolopha"             "Phasianus_colchicus"            
[183] "Chrysolophus_pictus"             "Lophura_nycthemera"             
[185] "Lophura_ignita"                  "Syrmaticus_ellioti"             
[187] "Syrmaticus_reevesii"             "Perdix_perdix"                  
[189] "Tetrao_urogallus"                "Lagopus_muta"                   
[191] "Lagopus_lagopus"                 "Lophophorus_impejanus"          
[193] "Tragopan_temminckii"             "Pavo_cristatus"                 
[195] "Gallus_gallus"                   "Gallus_sonneratii"              
[197] "Rollulus_rouloul"                "Arborophila_torqueola"          
[199] "Numida_meleagris"               

setdiff(dat_organ$phylo, tree$tip.label)      # Database species absent in tree

character(0)

# Exclude mismatched species for consistency
tree_organ <- keep.tip(tree, intersect(tree$tip.label, dat_organ$phylo))
dat_organ <- dat_organ[dat_organ$phylo %in% tree_organ$tip.label, ]

# Re-check for mismatches after pruning
setdiff(tree_organ$tip.label, dat_organ$phylo)

character(0)

setdiff(dat_organ$phylo, tree_organ$tip.label)

character(0)

# Is ultrametric?
is.ultrametric(tree_organ)

[1] TRUE

# how many species?
length(tree_organ$tip.label)

[1] 5

# Compute phylogenetic covariance matrix
A_organ <- ape::vcv.phylo(tree_organ, corr = TRUE)

Model simple

model_simple_pituitary_glands <- brm(
  log10_organ_size ~ 
    1 + 
    log10_body_size +
    (1 + log10_body_size | sex),
  data = dat_organ,
  family = gaussian(),
    prior = c(
    prior(normal(0.75, 0.5), class = "b", coef = "log10_body_size"),
    prior(normal(0, 2), class = "Intercept"),
    prior(student_t(3, 0, 0.5), class = "sd"),
    prior(student_t(3, 0, 1),   class = "sigma")
  ),
  seed = 6955,
  sample_prior = TRUE, 
  chains = 4, 
  cores = 4, 
  threads = threading(2),
  iter = 4000, 
  warmup = 2000,
  control = list(max_treedepth = 15,
                 adapt_delta = 0.99),
  save_pars = save_pars(all = TRUE),
  silent = TRUE, refresh = 0
)

Running MCMC with 4 parallel chains, with 2 thread(s) per chain...

Chain 4 finished in 3.9 seconds.
Chain 3 finished in 4.0 seconds.
Chain 1 finished in 4.7 seconds.
Chain 2 finished in 4.6 seconds.

All 4 chains finished successfully.
Mean chain execution time: 4.3 seconds.
Total execution time: 4.7 seconds.

Model check

pp_check(model_simple_pituitary_glands)

Model summary

summary(model_simple_pituitary_glands)

 Family: gaussian 
  Links: mu = identity; sigma = identity 
Formula: log10_organ_size ~ 1 + log10_body_size + (1 + log10_body_size | sex) 
   Data: dat_organ (Number of observations: 10) 
  Draws: 4 chains, each with iter = 4000; warmup = 2000; thin = 1;
         total post-warmup draws = 8000

Multilevel Hyperparameters:
~sex (Number of levels: 2) 
                               Estimate Est.Error l-95% CI u-95% CI Rhat
sd(Intercept)                      0.31      0.32     0.01     1.19 1.00
sd(log10_body_size)                0.18      0.20     0.00     0.75 1.00
cor(Intercept,log10_body_size)    -0.07      0.60    -0.97     0.95 1.00
                               Bulk_ESS Tail_ESS
sd(Intercept)                      4018     3598
sd(log10_body_size)                1788     3113
cor(Intercept,log10_body_size)     4215     4178

Regression Coefficients:
                Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept          -3.74      0.34    -4.36    -2.98 1.00     4347     4113
log10_body_size     0.75      0.16     0.46     1.12 1.00     2277     1588

Further Distributional Parameters:
      Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma     0.10      0.03     0.05     0.18 1.00     4141     4111

Draws were sampled using sample(hmc). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).

I will next extract, for each sex, the estimated slope and intercept, together with the 95% credible intervals.

# Extract combined coefficients (fixed + random)
coef(model_simple_pituitary_glands)$sex %>%
{tibble(
  sex = dimnames(.)[[1]],
  intercept    = .[, "Estimate", "Intercept"],
  intercept_low  = .[, "Q2.5", "Intercept"], 
  intercept_high = .[, "Q97.5", "Intercept"]
)} %>%
bind_cols(
  tibble(
    sex = dimnames(coef(model_simple_pituitary_glands)$sex)[[1]],
    slope = coef(model_simple_pituitary_glands)$sex[, "Estimate", "log10_body_size"]
  ) %>% select(slope),
  tibble(
    sex = dimnames(coef(model_simple_pituitary_glands)$sex)[[1]],
    slope_low  = coef(model_simple_pituitary_glands)$sex[, "Q2.5", "log10_body_size"],
    slope_high = coef(model_simple_pituitary_glands)$sex[, "Q97.5", "log10_body_size"]
  ) %>% select(slope_low, slope_high)
)

# A tibble: 2 × 7
  sex    intercept intercept_low intercept_high slope slope_low slope_high
  <chr>      <dbl>         <dbl>          <dbl> <dbl>     <dbl>      <dbl>
1 female     -3.75         -4.20          -3.31 0.731     0.571      0.892
2 male       -3.79         -4.21          -3.36 0.714     0.567      0.860

Model with phylogeny

model_phylo_pituitary_glands <- brm(
  log10_organ_size ~ 
    1 + 
    log10_body_size +
    (1 + log10_body_size | sex) +
    (1 | gr(phylo, cov = A_organ)),
  data = dat_organ,
  data2 = list(A_organ = A_organ),
  family = gaussian(),
    prior = c(
    prior(normal(0.75, 0.5), class = "b", coef = "log10_body_size"),
    prior(normal(0, 2), class = "Intercept"),
    prior(student_t(3, 0, 0.5), class = "sd"),
    prior(student_t(3, 0, 1),   class = "sigma")
  ),
  seed = 6955,
  sample_prior = TRUE, 
  chains = 4, 
  cores = 4, 
  threads = threading(2),
  iter = 4000, 
  warmup = 2000,
  control = list(max_treedepth = 15,
                 adapt_delta = 0.99),
  save_pars = save_pars(all = TRUE),
  silent = TRUE, refresh = 0
)

Running MCMC with 4 parallel chains, with 2 thread(s) per chain...

Chain 2 finished in 33.0 seconds.
Chain 4 finished in 43.5 seconds.
Chain 1 finished in 54.5 seconds.
Chain 3 finished in 96.6 seconds.

All 4 chains finished successfully.
Mean chain execution time: 56.9 seconds.
Total execution time: 96.8 seconds.

Model check

pp_check(model_phylo_pituitary_glands)

Model summary

summary(model_phylo_pituitary_glands)

 Family: gaussian 
  Links: mu = identity; sigma = identity 
Formula: log10_organ_size ~ 1 + log10_body_size + (1 + log10_body_size | sex) + (1 | gr(phylo, cov = A_organ)) 
   Data: dat_organ (Number of observations: 10) 
  Draws: 4 chains, each with iter = 4000; warmup = 2000; thin = 1;
         total post-warmup draws = 8000

Multilevel Hyperparameters:
~phylo (Number of levels: 5) 
              Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept)     0.16      0.10     0.05     0.40 1.00     2063     2185

~sex (Number of levels: 2) 
                               Estimate Est.Error l-95% CI u-95% CI Rhat
sd(Intercept)                      0.24      0.29     0.01     1.04 1.00
sd(log10_body_size)                0.18      0.20     0.00     0.73 1.00
cor(Intercept,log10_body_size)    -0.05      0.61    -0.98     0.96 1.00
                               Bulk_ESS Tail_ESS
sd(Intercept)                      4165     4489
sd(log10_body_size)                2562     3028
cor(Intercept,log10_body_size)     5442     4775

Regression Coefficients:
                Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept          -3.83      0.45    -4.70    -2.92 1.00     2667     3522
log10_body_size     0.78      0.18     0.46     1.19 1.00     2415     2626

Further Distributional Parameters:
      Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma     0.03      0.02     0.01     0.07 1.00      768     1777

Draws were sampled using sample(hmc). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).

Phylogenetic signal

hyp <- paste(
  "sd_phylo__Intercept^2 /",
  "(sd_phylo__Intercept^2 + sd_sex__Intercept^2 + sigma^2) = 0"
)
(hyp <- hypothesis(model_phylo_pituitary_glands, hyp, class = NULL))

Hypothesis Tests for class :
                Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
1 (sd_phylo__Interc... = 0     0.49      0.35     0.01     0.99       0.32
  Post.Prob Star
1      0.24    *
---
'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
'*': For one-sided hypotheses, the posterior probability exceeds 95%;
for two-sided hypotheses, the value tested against lies outside the 95%-CI.
Posterior probabilities of point hypotheses assume equal prior probabilities.

lambda_pituitary_glands <- hyp$hypothesis$Estimate

I will next extract, for each sex, the estimated slope and intercept, together with the 95% credible intervals.

# Extract combined coefficients (fixed + random)
coef(model_phylo_pituitary_glands)$sex %>%
{tibble(
  sex = dimnames(.)[[1]],
  intercept    = .[, "Estimate", "Intercept"],
  intercept_low  = .[, "Q2.5", "Intercept"], 
  intercept_high = .[, "Q97.5", "Intercept"]
)} %>%
bind_cols(
  tibble(
    sex = dimnames(coef(model_phylo_pituitary_glands)$sex)[[1]],
    slope = coef(model_phylo_pituitary_glands)$sex[, "Estimate", "log10_body_size"]
  ) %>% select(slope),
  tibble(
    sex = dimnames(coef(model_phylo_pituitary_glands)$sex)[[1]],
    slope_low  = coef(model_phylo_pituitary_glands)$sex[, "Q2.5", "log10_body_size"],
    slope_high = coef(model_phylo_pituitary_glands)$sex[, "Q97.5", "log10_body_size"]
  ) %>% select(slope_low, slope_high)
)

# A tibble: 2 × 7
  sex    intercept intercept_low intercept_high slope slope_low slope_high
  <chr>      <dbl>         <dbl>          <dbl> <dbl>     <dbl>      <dbl>
1 female     -3.85         -4.64          -3.11 0.775     0.524      1.04 
2 male       -3.85         -4.56          -3.15 0.745     0.517      0.973

Model comparison

loo_simple <- loo(model_simple_pituitary_glands)
loo_phylo <- loo(model_phylo_pituitary_glands)
loo_compare(loo_simple, loo_phylo)

                              elpd_diff se_diff
model_phylo_pituitary_glands    0.0       0.0  
model_simple_pituitary_glands -11.8       1.6  

In this comparison, the phylogenetic model is clearly preferable to the model treating species as independent observational units. The phylogenetic model (model_phylo_pituitary_glands) serves as reference with elpd_diff = 0, while the simpler model (model_simple_pituitary_glands) has an expected log predictive density (ELPD) that is about 11.8 units lower, with an associated standard error of 1.6. In leave-one-out cross-validation, differences exceeding approximately four times their standard error indicate strong evidence. Here, 11.8/1.6≈7.4, indicating a large difference relative to its uncertainty, and thus providing evidence favouring the phylogenetic model.

Spleen

Filter data and prune tree

# Filter organ of interest
dat_organ <- dat_mean %>%
  group_by(organ_grouped, sex) %>%
  ungroup() %>%
  filter(organ_grouped == "spleen")

# Check for database/tree species mismatches
setdiff(tree$tip.label, dat_organ$phylo)      # Tree species absent in database

  [1] "Petrochromis_famula"             "Lobochilotes_labiatus"          
  [3] "Simochromis_diagramma"           "Petrochromis_orthognathus"      
  [5] "Ctenochromis_horei"              "Limnotilapia_dardennii"         
  [7] "Gnathochromis_pfefferi"          "Tropheus_moorii"                
  [9] "Tropheus_brichardi"              "Haplotaxodon_microlepis"        
 [11] "Perissodus_microlepis"           "Benthochromis_tricoti"          
 [13] "Cyprichromis_leptosoma"          "Greenwoodochromis_christyi"     
 [15] "Limnochromis_staneri"            "Gnathochromis_permaxillaris"    
 [17] "Baileychromis_centropomoides"    "Triglachromis_otostigma"        
 [19] "Cyphotilapia_frontosa"           "Ophthalmotilapia_ventralis"     
 [21] "Cyathopharynx_furcifer"          "Ophthalmotilapia_nasuta"        
 [23] "Ophthalmotilapia_boops"          "Aulonocranus_dewindti"          
 [25] "Ectodus_descampsii"              "Callochromis_melanostigma"      
 [27] "Xenotilapia_melanogenys"         "Xenotilapia_flavipinnis"        
 [29] "Eretmodus_cyanostictus"          "Tanganicodus_irsacae"           
 [31] "Spathodus_marlieri"              "Spathodus_erythrodon"           
 [33] "Neolamprologus_brichardi"        "Julidochromis_regani"           
 [35] "Julidochromis_marlieri"          "Neolamprologus_tetracanthus"    
 [37] "Telmatochromis_temporalis"       "Lepidiolamprologus_elongatus"   
 [39] "Lepidiolamprologus_profundicola" "Lepidiolamprologus_nkambae"     
 [41] "Altolamprologus_compressiceps"   "Neolamprologus_brevis"          
 [43] "Chalinochromis_brichardi"        "Julidochromis_ornatus"          
 [45] "Lamprologus_ornatipinnis"        "Neolamprologus_pulcher"         
 [47] "Variabilichromis_moorii"         "Neolamprologus_tretocephalus"   
 [49] "Neolamprologus_sexfasciatus"     "Trematocara_unimaculatum"       
 [51] "Hemibates_stenosoma"             "Bathybates_ferox"               
 [53] "Oreochromis_niloticus"           "Poecilia_reticulata"            
 [55] "Nerophis_lumbriciformis"         "Syngnathus_abaster"             
 [57] "Syngnathus_schlegeli"            "Hippocampus_comes"              
 [59] "Hippocampus_trimaculatus"        "Hippocampus_kuda"               
 [61] "Hippocampus_spinosissimus"       "Hippocampus_abdominalis"        
 [63] "Hippichthys_cyanospilos"         "Syngnathoides_biaculeatus"      
 [65] "Corythoichthys_intestinalis"     "Corythoichthys_haematopterus"   
 [67] "Doryichthys_boaja"               "Doryrhamphus_japonicus"         
 [69] "Entelurus_aequoreus"             "Anguilla_anguilla"              
 [71] "Syncerus_caffer"                 "Tragelaphus_eurycerus"          
 [73] "Tragelaphus_scriptus"            "Redunca_arundinum"              
 [75] "Antidorcas_marsupialis"          "Nanger_granti"                  
 [77] "Raphicerus_campestris"           "Cephalophus_natalensis"         
 [79] "Sylvicapra_grimmia"              "Oreotragus_oreotragus"          
 [81] "Hippotragus_equinus"             "Addax_nasomaculatus"            
 [83] "Oryx_gazella"                    "Connochaetes_taurinus"          
 [85] "Damaliscus_lunatus"              "Ovis_aries"                     
 [87] "Aepyceros_melampus"              "Pteropus_alecto"                
 [89] "Pteropus_poliocephalus"          "Pteropus_scapulatus"            
 [91] "Chlorocebus_aethiops"            "Chlorocebus_sabaeus"            
 [93] "Erythrocebus_patas"              "Papio_cynocephalus"             
 [95] "Papio_anubis"                    "Cercocebus_atys"                
 [97] "Macaca_arctoides"                "Macaca_mulatta"                 
 [99] "Macaca_maura"                    "Trachypithecus_francoisi"       
[101] "Phrynocephalus_vlangalii"        "Platycercus_caledonicus"        
[103] "Platycercus_elegans"             "Platycercus_eximius"            
[105] "Platycercus_venustus"            "Barnardius_zonarius"            
[107] "Northiella_haematogaster"        "Lathamus_discolor"              
[109] "Neophema_chrysostoma"            "Neophema_pulchella"             
[111] "Psittacula_krameri"              "Eclectus_roratus"               
[113] "Aprosmictus_jonquillaceus"       "Alisterus_scapularis"           
[115] "Alisterus_amboinensis"           "Polytelis_alexandrae"           
[117] "Trichoglossus_haematodus"        "Agapornis_lilianae"             
[119] "Agapornis_taranta"               "Loriculus_vernalis"             
[121] "Ara_ararauna"                    "Guaruba_guarouba"               
[123] "Enicognathus_leptorhynchus"      "Pionites_melanocephalus"        
[125] "Forpus_coelestis"                "Forpus_passerinus"              
[127] "Amazona_leucocephala"            "Amazona_albifrons"              
[129] "Amazona_pretrei"                 "Amazona_vinacea"                
[131] "Amazona_finschi"                 "Amazona_amazonica"              
[133] "Amazona_ochrocephala"            "Amazona_aestiva"                
[135] "Brotogeris_versicolurus"         "Brotogeris_pyrrhoptera"         
[137] "Bolborhynchus_lineola"           "Poicephalus_gulielmi"           
[139] "Poicephalus_meyeri"              "Psittacus_erithacus"            
[141] "Serinus_mennelli"                "Padda_oryzivora"                
[143] "Lonchura_punctulata"             "Lonchura_flaviprymna"           
[145] "Lonchura_bicolor"                "Hypargos_niveoguttatus"         
[147] "Pytilia_hypogrammica"            "Uraeginthus_bengalus"           
[149] "Amandava_amandava"               "Plectrophenax_nivalis"          
[151] "Serinus_canaria"                 "Serinus_serinus"                
[153] "Loxia_curvirostra"               "Carduelis_carduelis"            
[155] "Carpodacus_roseus"               "Uragus_sibiricus"               
[157] "Pyrrhula_pyrrhula"               "Pinicola_enucleator"            
[159] "Bucanetes_githagineus"           "Coccothraustes_coccothraustes"  
[161] "Mycerobas_affinis"               "Mycerobas_carnipes"             
[163] "Fringilla_montifringilla"        "Fringilla_coelebs"              
[165] "Anas_acuta"                      "Anas_crecca"                    
[167] "Mergus_serrator"                 "Mergus_merganser"               
[169] "Bucephala_clangula"              "Melanitta_nigra"                
[171] "Somateria_mollissima"            "Callonetta_leucophrys"          
[173] "Branta_bernicla"                 "Branta_leucopsis"               
[175] "Anser_anser"                     "Cygnus_columbianus"             
[177] "Tadorna_tadorna"                 "Pucrasia_macrolopha"            
[179] "Phasianus_colchicus"             "Chrysolophus_pictus"            
[181] "Lophura_nycthemera"              "Lophura_ignita"                 
[183] "Syrmaticus_ellioti"              "Syrmaticus_reevesii"            
[185] "Perdix_perdix"                   "Tetrao_urogallus"               
[187] "Lagopus_muta"                    "Lagopus_lagopus"                
[189] "Lophophorus_impejanus"           "Tragopan_temminckii"            
[191] "Pavo_cristatus"                  "Gallus_sonneratii"              
[193] "Rollulus_rouloul"                "Arborophila_torqueola"          
[195] "Numida_meleagris"               

setdiff(dat_organ$phylo, tree$tip.label)      # Database species absent in tree

character(0)

# Exclude mismatched species for consistency
tree_organ <- keep.tip(tree, intersect(tree$tip.label, dat_organ$phylo))
dat_organ <- dat_organ[dat_organ$phylo %in% tree_organ$tip.label, ]

# Re-check for mismatches after pruning
setdiff(tree_organ$tip.label, dat_organ$phylo)

character(0)

setdiff(dat_organ$phylo, tree_organ$tip.label)

character(0)

# Is ultrametric?
is.ultrametric(tree_organ)

[1] TRUE

# how many species?
length(tree_organ$tip.label)

[1] 9

# Compute phylogenetic covariance matrix
A_organ <- ape::vcv.phylo(tree_organ, corr = TRUE)

Model simple

model_simple_spleen <- brm(
  log10_organ_size ~ 
    1 + 
    log10_body_size +
    (1 + log10_body_size | sex),
  data = dat_organ,
  family = gaussian(),
    prior = c(
    prior(normal(0.75, 0.5), class = "b", coef = "log10_body_size"),
    prior(normal(0, 2), class = "Intercept"),
    prior(student_t(3, 0, 0.5), class = "sd"),
    prior(student_t(3, 0, 1),   class = "sigma")
  ),
  seed = 6955,
  sample_prior = TRUE, 
  chains = 4, 
  cores = 4, 
  threads = threading(2),
  iter = 4000, 
  warmup = 2000,
  control = list(max_treedepth = 15,
                 adapt_delta = 0.99),
  save_pars = save_pars(all = TRUE),
  silent = TRUE, refresh = 0
)

Running MCMC with 4 parallel chains, with 2 thread(s) per chain...

Chain 1 finished in 1.4 seconds.
Chain 2 finished in 2.0 seconds.
Chain 4 finished in 2.1 seconds.
Chain 3 finished in 2.5 seconds.

All 4 chains finished successfully.
Mean chain execution time: 2.0 seconds.
Total execution time: 2.7 seconds.

Model check

pp_check(model_simple_spleen)

Model summary

summary(model_simple_spleen)

 Family: gaussian 
  Links: mu = identity; sigma = identity 
Formula: log10_organ_size ~ 1 + log10_body_size + (1 + log10_body_size | sex) 
   Data: dat_organ (Number of observations: 18) 
  Draws: 4 chains, each with iter = 4000; warmup = 2000; thin = 1;
         total post-warmup draws = 8000

Multilevel Hyperparameters:
~sex (Number of levels: 2) 
                               Estimate Est.Error l-95% CI u-95% CI Rhat
sd(Intercept)                      0.32      0.32     0.01     1.14 1.00
sd(log10_body_size)                0.20      0.22     0.00     0.82 1.00
cor(Intercept,log10_body_size)    -0.10      0.59    -0.97     0.94 1.00
                               Bulk_ESS Tail_ESS
sd(Intercept)                      3318     3175
sd(log10_body_size)                2302     3173
cor(Intercept,log10_body_size)     4118     4275

Regression Coefficients:
                Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept          -3.01      0.39    -3.77    -2.18 1.00     4839     4271
log10_body_size     0.99      0.18     0.60     1.34 1.00     2407     1968

Further Distributional Parameters:
      Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma     0.38      0.08     0.27     0.56 1.00     5903     4940

Draws were sampled using sample(hmc). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).

I will next extract, for each sex, the estimated slope and intercept, together with the 95% credible intervals.

# Extract combined coefficients (fixed + random)
coef(model_simple_spleen)$sex %>%
{tibble(
  sex = dimnames(.)[[1]],
  intercept    = .[, "Estimate", "Intercept"],
  intercept_low  = .[, "Q2.5", "Intercept"], 
  intercept_high = .[, "Q97.5", "Intercept"]
)} %>%
bind_cols(
  tibble(
    sex = dimnames(coef(model_simple_spleen)$sex)[[1]],
    slope = coef(model_simple_spleen)$sex[, "Estimate", "log10_body_size"]
  ) %>% select(slope),
  tibble(
    sex = dimnames(coef(model_simple_spleen)$sex)[[1]],
    slope_low  = coef(model_simple_spleen)$sex[, "Q2.5", "log10_body_size"],
    slope_high = coef(model_simple_spleen)$sex[, "Q97.5", "log10_body_size"]
  ) %>% select(slope_low, slope_high)
)

# A tibble: 2 × 7
  sex    intercept intercept_low intercept_high slope slope_low slope_high
  <chr>      <dbl>         <dbl>          <dbl> <dbl>     <dbl>      <dbl>
1 female     -3.01         -3.58          -2.43  1.01     0.771       1.24
2 male       -3.06         -3.63          -2.49  1.02     0.787       1.25

Model with phylogeny

model_phylo_spleen <- brm(
  log10_organ_size ~ 
    1 + 
    log10_body_size +
    (1 + log10_body_size | sex) +
    (1 | gr(phylo, cov = A_organ)),
  data = dat_organ,
  data2 = list(A_organ = A_organ),
  family = gaussian(),
    prior = c(
    prior(normal(0.75, 0.5), class = "b", coef = "log10_body_size"),
    prior(normal(0, 2), class = "Intercept"),
    prior(student_t(3, 0, 0.5), class = "sd"),
    prior(student_t(3, 0, 1),   class = "sigma")
  ),
  seed = 6955,
  sample_prior = TRUE, 
  chains = 4, 
  cores = 4, 
  threads = threading(2),
  iter = 4000, 
  warmup = 2000,
  control = list(max_treedepth = 15,
                 adapt_delta = 0.99),
  save_pars = save_pars(all = TRUE),
  silent = TRUE, refresh = 0
)

Running MCMC with 4 parallel chains, with 2 thread(s) per chain...

Chain 4 finished in 15.2 seconds.
Chain 2 finished in 15.4 seconds.
Chain 1 finished in 20.5 seconds.
Chain 3 finished in 26.5 seconds.

All 4 chains finished successfully.
Mean chain execution time: 19.4 seconds.
Total execution time: 26.6 seconds.

Model check

pp_check(model_phylo_spleen)

Model summary

summary(model_phylo_spleen)

 Family: gaussian 
  Links: mu = identity; sigma = identity 
Formula: log10_organ_size ~ 1 + log10_body_size + (1 + log10_body_size | sex) + (1 | gr(phylo, cov = A_organ)) 
   Data: dat_organ (Number of observations: 18) 
  Draws: 4 chains, each with iter = 4000; warmup = 2000; thin = 1;
         total post-warmup draws = 8000

Multilevel Hyperparameters:
~phylo (Number of levels: 9) 
              Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept)     1.18      0.37     0.57     2.02 1.00     1063      691

~sex (Number of levels: 2) 
                               Estimate Est.Error l-95% CI u-95% CI Rhat
sd(Intercept)                      0.29      0.30     0.01     1.10 1.00
sd(log10_body_size)                0.18      0.23     0.00     0.76 1.00
cor(Intercept,log10_body_size)    -0.12      0.59    -0.98     0.94 1.00
                               Bulk_ESS Tail_ESS
sd(Intercept)                      3272     3361
sd(log10_body_size)                2506     3534
cor(Intercept,log10_body_size)     5019     4860

Regression Coefficients:
                Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept          -2.76      0.89    -4.42    -0.83 1.00     2431     3941
log10_body_size     0.91      0.22     0.46     1.34 1.00     2433     3989

Further Distributional Parameters:
      Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma     0.09      0.05     0.04     0.25 1.00      779      625

Draws were sampled using sample(hmc). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).

Phylogenetic signal

hyp <- paste(
  "sd_phylo__Intercept^2 /",
  "(sd_phylo__Intercept^2 + sd_sex__Intercept^2 + sigma^2) = 0"
)
(hyp <- hypothesis(model_phylo_spleen, hyp, class = NULL))

Hypothesis Tests for class :
                Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
1 (sd_phylo__Interc... = 0     0.89      0.16     0.37        1       0.01
  Post.Prob Star
1      0.01    *
---
'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
'*': For one-sided hypotheses, the posterior probability exceeds 95%;
for two-sided hypotheses, the value tested against lies outside the 95%-CI.
Posterior probabilities of point hypotheses assume equal prior probabilities.

lambda_spleen <- hyp$hypothesis$Estimate

I will next extract, for each sex, the estimated slope and intercept, together with the 95% credible intervals.

# Extract combined coefficients (fixed + random)
coef(model_phylo_spleen)$sex %>%
{tibble(
  sex = dimnames(.)[[1]],
  intercept    = .[, "Estimate", "Intercept"],
  intercept_low  = .[, "Q2.5", "Intercept"], 
  intercept_high = .[, "Q97.5", "Intercept"]
)} %>%
bind_cols(
  tibble(
    sex = dimnames(coef(model_phylo_spleen)$sex)[[1]],
    slope = coef(model_phylo_spleen)$sex[, "Estimate", "log10_body_size"]
  ) %>% select(slope),
  tibble(
    sex = dimnames(coef(model_phylo_spleen)$sex)[[1]],
    slope_low  = coef(model_phylo_spleen)$sex[, "Q2.5", "log10_body_size"],
    slope_high = coef(model_phylo_spleen)$sex[, "Q97.5", "log10_body_size"]
  ) %>% select(slope_low, slope_high)
)

# A tibble: 2 × 7
  sex    intercept intercept_low intercept_high slope slope_low slope_high
  <chr>      <dbl>         <dbl>          <dbl> <dbl>     <dbl>      <dbl>
1 female     -2.71         -4.35         -0.851 0.906     0.494       1.26
2 male       -2.81         -4.43         -0.965 0.937     0.547       1.28

Model comparison

loo_simple <- loo(model_simple_spleen)
loo_phylo <- loo(model_phylo_spleen)
loo_compare(loo_simple, loo_phylo)

                    elpd_diff se_diff
model_phylo_spleen    0.0       0.0  
model_simple_spleen -21.4       1.3  

In this comparison, the phylogenetic model is clearly preferable to the model treating species as independent observational units. The phylogenetic model (model_phylo_spleen) serves as reference with elpd_diff = 0, while the simpler model (model_simple_spleen) has an expected log predictive density (ELPD) 21.4 units lower, with an associated standard error of 1.3. In leave-one-out cross-validation, differences exceeding approximately four times their standard error indicate strong evidence. Here, 21.4/1.3≈16, indicating a very large difference relative to its uncertainty, and thus providing very strong evidence favouring the phylogenetic model.

Stomach

Filter data and prune tree

# Filter organ of interest
dat_organ <- dat_mean %>%
  group_by(organ_grouped, sex) %>%
  ungroup() %>%
  filter(organ_grouped == "stomach")

# Check for database/tree species mismatches
setdiff(tree$tip.label, dat_organ$phylo)      # Tree species absent in database

  [1] "Petrochromis_famula"             "Lobochilotes_labiatus"          
  [3] "Simochromis_diagramma"           "Petrochromis_orthognathus"      
  [5] "Ctenochromis_horei"              "Limnotilapia_dardennii"         
  [7] "Gnathochromis_pfefferi"          "Tropheus_moorii"                
  [9] "Tropheus_brichardi"              "Haplotaxodon_microlepis"        
 [11] "Perissodus_microlepis"           "Benthochromis_tricoti"          
 [13] "Cyprichromis_leptosoma"          "Greenwoodochromis_christyi"     
 [15] "Limnochromis_staneri"            "Gnathochromis_permaxillaris"    
 [17] "Baileychromis_centropomoides"    "Triglachromis_otostigma"        
 [19] "Cyphotilapia_frontosa"           "Ophthalmotilapia_ventralis"     
 [21] "Cyathopharynx_furcifer"          "Ophthalmotilapia_nasuta"        
 [23] "Ophthalmotilapia_boops"          "Aulonocranus_dewindti"          
 [25] "Ectodus_descampsii"              "Callochromis_melanostigma"      
 [27] "Xenotilapia_melanogenys"         "Xenotilapia_flavipinnis"        
 [29] "Eretmodus_cyanostictus"          "Tanganicodus_irsacae"           
 [31] "Spathodus_marlieri"              "Spathodus_erythrodon"           
 [33] "Neolamprologus_brichardi"        "Julidochromis_regani"           
 [35] "Julidochromis_marlieri"          "Neolamprologus_tetracanthus"    
 [37] "Telmatochromis_temporalis"       "Lepidiolamprologus_elongatus"   
 [39] "Lepidiolamprologus_profundicola" "Lepidiolamprologus_nkambae"     
 [41] "Altolamprologus_compressiceps"   "Neolamprologus_brevis"          
 [43] "Chalinochromis_brichardi"        "Julidochromis_ornatus"          
 [45] "Lamprologus_ornatipinnis"        "Neolamprologus_pulcher"         
 [47] "Variabilichromis_moorii"         "Neolamprologus_tretocephalus"   
 [49] "Neolamprologus_sexfasciatus"     "Trematocara_unimaculatum"       
 [51] "Hemibates_stenosoma"             "Bathybates_ferox"               
 [53] "Oreochromis_niloticus"           "Poecilia_reticulata"            
 [55] "Nerophis_lumbriciformis"         "Syngnathus_abaster"             
 [57] "Syngnathus_schlegeli"            "Hippocampus_comes"              
 [59] "Hippocampus_trimaculatus"        "Hippocampus_kuda"               
 [61] "Hippocampus_spinosissimus"       "Hippocampus_abdominalis"        
 [63] "Hippichthys_cyanospilos"         "Syngnathoides_biaculeatus"      
 [65] "Corythoichthys_intestinalis"     "Corythoichthys_haematopterus"   
 [67] "Doryichthys_boaja"               "Doryrhamphus_japonicus"         
 [69] "Entelurus_aequoreus"             "Anguilla_anguilla"              
 [71] "Syncerus_caffer"                 "Tragelaphus_eurycerus"          
 [73] "Tragelaphus_scriptus"            "Redunca_arundinum"              
 [75] "Antidorcas_marsupialis"          "Nanger_granti"                  
 [77] "Raphicerus_campestris"           "Cephalophus_natalensis"         
 [79] "Sylvicapra_grimmia"              "Oreotragus_oreotragus"          
 [81] "Hippotragus_equinus"             "Addax_nasomaculatus"            
 [83] "Oryx_gazella"                    "Connochaetes_taurinus"          
 [85] "Damaliscus_lunatus"              "Ovis_aries"                     
 [87] "Aepyceros_melampus"              "Pteropus_alecto"                
 [89] "Pteropus_poliocephalus"          "Pteropus_scapulatus"            
 [91] "Rattus_norvegicus"               "Chlorocebus_aethiops"           
 [93] "Chlorocebus_sabaeus"             "Erythrocebus_patas"             
 [95] "Papio_cynocephalus"              "Papio_anubis"                   
 [97] "Cercocebus_atys"                 "Macaca_arctoides"               
 [99] "Macaca_mulatta"                  "Macaca_fascicularis"            
[101] "Macaca_maura"                    "Trachypithecus_francoisi"       
[103] "Platycercus_caledonicus"         "Platycercus_elegans"            
[105] "Platycercus_eximius"             "Platycercus_venustus"           
[107] "Barnardius_zonarius"             "Northiella_haematogaster"       
[109] "Lathamus_discolor"               "Neophema_chrysostoma"           
[111] "Neophema_pulchella"              "Psittacula_krameri"             
[113] "Eclectus_roratus"                "Aprosmictus_jonquillaceus"      
[115] "Alisterus_scapularis"            "Alisterus_amboinensis"          
[117] "Polytelis_alexandrae"            "Trichoglossus_haematodus"       
[119] "Agapornis_lilianae"              "Agapornis_taranta"              
[121] "Loriculus_vernalis"              "Ara_ararauna"                   
[123] "Guaruba_guarouba"                "Enicognathus_leptorhynchus"     
[125] "Pionites_melanocephalus"         "Forpus_coelestis"               
[127] "Forpus_passerinus"               "Amazona_leucocephala"           
[129] "Amazona_albifrons"               "Amazona_pretrei"                
[131] "Amazona_vinacea"                 "Amazona_finschi"                
[133] "Amazona_amazonica"               "Amazona_ochrocephala"           
[135] "Amazona_aestiva"                 "Brotogeris_versicolurus"        
[137] "Brotogeris_pyrrhoptera"          "Bolborhynchus_lineola"          
[139] "Poicephalus_gulielmi"            "Poicephalus_meyeri"             
[141] "Psittacus_erithacus"             "Serinus_mennelli"               
[143] "Ficedula_hypoleuca"              "Padda_oryzivora"                
[145] "Lonchura_punctulata"             "Lonchura_flaviprymna"           
[147] "Lonchura_bicolor"                "Hypargos_niveoguttatus"         
[149] "Pytilia_hypogrammica"            "Uraeginthus_bengalus"           
[151] "Amandava_amandava"               "Plectrophenax_nivalis"          
[153] "Serinus_canaria"                 "Serinus_serinus"                
[155] "Loxia_curvirostra"               "Carduelis_carduelis"            
[157] "Carpodacus_roseus"               "Uragus_sibiricus"               
[159] "Pyrrhula_pyrrhula"               "Pinicola_enucleator"            
[161] "Bucanetes_githagineus"           "Coccothraustes_coccothraustes"  
[163] "Mycerobas_affinis"               "Mycerobas_carnipes"             
[165] "Fringilla_montifringilla"        "Fringilla_coelebs"              
[167] "Anas_acuta"                      "Anas_crecca"                    
[169] "Mergus_serrator"                 "Mergus_merganser"               
[171] "Bucephala_clangula"              "Melanitta_nigra"                
[173] "Somateria_mollissima"            "Callonetta_leucophrys"          
[175] "Branta_bernicla"                 "Branta_leucopsis"               
[177] "Anser_anser"                     "Cygnus_columbianus"             
[179] "Tadorna_tadorna"                 "Pucrasia_macrolopha"            
[181] "Phasianus_colchicus"             "Chrysolophus_pictus"            
[183] "Lophura_nycthemera"              "Lophura_ignita"                 
[185] "Syrmaticus_ellioti"              "Syrmaticus_reevesii"            
[187] "Perdix_perdix"                   "Tetrao_urogallus"               
[189] "Lagopus_muta"                    "Lagopus_lagopus"                
[191] "Lophophorus_impejanus"           "Tragopan_temminckii"            
[193] "Pavo_cristatus"                  "Gallus_sonneratii"              
[195] "Rollulus_rouloul"                "Arborophila_torqueola"          

setdiff(dat_organ$phylo, tree$tip.label)      # Database species absent in tree

character(0)

# Exclude mismatched species for consistency
tree_organ <- keep.tip(tree, intersect(tree$tip.label, dat_organ$phylo))
dat_organ <- dat_organ[dat_organ$phylo %in% tree_organ$tip.label, ]

# Re-check for mismatches after pruning
setdiff(tree_organ$tip.label, dat_organ$phylo)

character(0)

setdiff(dat_organ$phylo, tree_organ$tip.label)

character(0)

# Is ultrametric?
is.ultrametric(tree_organ)

[1] TRUE

# how many species?
length(tree_organ$tip.label)

[1] 8

# Compute phylogenetic covariance matrix
A_organ <- ape::vcv.phylo(tree_organ, corr = TRUE)

Model simple

model_simple_stomach <- brm(
  log10_organ_size ~ 
    1 + 
    log10_body_size +
    (1 + log10_body_size | sex),
  data = dat_organ,
  family = gaussian(),
    prior = c(
    prior(normal(0.75, 0.5), class = "b", coef = "log10_body_size"),
    prior(normal(0, 2), class = "Intercept"),
    prior(student_t(3, 0, 0.5), class = "sd"),
    prior(student_t(3, 0, 1),   class = "sigma")
  ),
  seed = 6955,
  sample_prior = TRUE, 
  chains = 4, 
  cores = 4, 
  threads = threading(2),
  iter = 4000, 
  warmup = 2000,
  control = list(max_treedepth = 15,
                 adapt_delta = 0.99),
  save_pars = save_pars(all = TRUE),
  silent = TRUE, refresh = 0
)

Running MCMC with 4 parallel chains, with 2 thread(s) per chain...

Chain 1 finished in 2.4 seconds.
Chain 3 finished in 2.5 seconds.
Chain 2 finished in 2.6 seconds.
Chain 4 finished in 2.6 seconds.

All 4 chains finished successfully.
Mean chain execution time: 2.5 seconds.
Total execution time: 2.8 seconds.

Model check

pp_check(model_simple_stomach)

Model summary

summary(model_simple_stomach)

 Family: gaussian 
  Links: mu = identity; sigma = identity 
Formula: log10_organ_size ~ 1 + log10_body_size + (1 + log10_body_size | sex) 
   Data: dat_organ (Number of observations: 16) 
  Draws: 4 chains, each with iter = 4000; warmup = 2000; thin = 1;
         total post-warmup draws = 8000

Multilevel Hyperparameters:
~sex (Number of levels: 2) 
                               Estimate Est.Error l-95% CI u-95% CI Rhat
sd(Intercept)                      0.29      0.30     0.01     1.08 1.00
sd(log10_body_size)                0.20      0.23     0.00     0.84 1.00
cor(Intercept,log10_body_size)    -0.09      0.60    -0.98     0.95 1.00
                               Bulk_ESS Tail_ESS
sd(Intercept)                      3636     3639
sd(log10_body_size)                1837     3384
cor(Intercept,log10_body_size)     3837     4182

Regression Coefficients:
                Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept          -2.63      0.33    -3.28    -1.95 1.00     4295     3726
log10_body_size     1.18      0.18     0.71     1.48 1.00     2080     1216

Further Distributional Parameters:
      Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma     0.23      0.05     0.15     0.35 1.00     5037     3724

Draws were sampled using sample(hmc). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).

I will next extract, for each sex, the estimated slope and intercept, together with the 95% credible intervals.

# Extract combined coefficients (fixed + random)
coef(model_simple_stomach)$sex %>%
{tibble(
  sex = dimnames(.)[[1]],
  intercept    = .[, "Estimate", "Intercept"],
  intercept_low  = .[, "Q2.5", "Intercept"], 
  intercept_high = .[, "Q97.5", "Intercept"]
)} %>%
bind_cols(
  tibble(
    sex = dimnames(coef(model_simple_stomach)$sex)[[1]],
    slope = coef(model_simple_stomach)$sex[, "Estimate", "log10_body_size"]
  ) %>% select(slope),
  tibble(
    sex = dimnames(coef(model_simple_stomach)$sex)[[1]],
    slope_low  = coef(model_simple_stomach)$sex[, "Q2.5", "log10_body_size"],
    slope_high = coef(model_simple_stomach)$sex[, "Q97.5", "log10_body_size"]
  ) %>% select(slope_low, slope_high)
)

# A tibble: 2 × 7
  sex    intercept intercept_low intercept_high slope slope_low slope_high
  <chr>      <dbl>         <dbl>          <dbl> <dbl>     <dbl>      <dbl>
1 female     -2.63         -3.03          -2.22  1.23      1.05       1.39
2 male       -2.64         -3.04          -2.23  1.23      1.06       1.39

Model with phylogeny

model_phylo_stomach <- brm(
  log10_organ_size ~ 
    1 + 
    log10_body_size +
    (1 + log10_body_size | sex) +
    (1 | gr(phylo, cov = A_organ)),
  data = dat_organ,
  data2 = list(A_organ = A_organ),
  family = gaussian(),
    prior = c(
    prior(normal(0.75, 0.5), class = "b", coef = "log10_body_size"),
    prior(normal(0, 2), class = "Intercept"),
    prior(student_t(3, 0, 0.5), class = "sd"),
    prior(student_t(3, 0, 1),   class = "sigma")
  ),
  seed = 6955,
  sample_prior = TRUE, 
  chains = 4, 
  cores = 4, 
  threads = threading(2),
  iter = 4000, 
  warmup = 2000,
  control = list(max_treedepth = 15,
                 adapt_delta = 0.99),
  save_pars = save_pars(all = TRUE),
  silent = TRUE, refresh = 0
)

Running MCMC with 4 parallel chains, with 2 thread(s) per chain...

Chain 2 finished in 14.5 seconds.
Chain 1 finished in 16.7 seconds.
Chain 4 finished in 17.1 seconds.
Chain 3 finished in 22.0 seconds.

All 4 chains finished successfully.
Mean chain execution time: 17.6 seconds.
Total execution time: 22.2 seconds.

Model check

pp_check(model_phylo_stomach)

Model summary

summary(model_phylo_stomach)

 Family: gaussian 
  Links: mu = identity; sigma = identity 
Formula: log10_organ_size ~ 1 + log10_body_size + (1 + log10_body_size | sex) + (1 | gr(phylo, cov = A_organ)) 
   Data: dat_organ (Number of observations: 16) 
  Draws: 4 chains, each with iter = 4000; warmup = 2000; thin = 1;
         total post-warmup draws = 8000

Multilevel Hyperparameters:
~phylo (Number of levels: 8) 
              Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept)     0.39      0.13     0.22     0.70 1.00     2453     4006

~sex (Number of levels: 2) 
                               Estimate Est.Error l-95% CI u-95% CI Rhat
sd(Intercept)                      0.21      0.27     0.00     0.93 1.00
sd(log10_body_size)                0.13      0.18     0.00     0.63 1.00
cor(Intercept,log10_body_size)    -0.05      0.62    -0.98     0.96 1.00
                               Bulk_ESS Tail_ESS
sd(Intercept)                      3348     3977
sd(log10_body_size)                2424     3143
cor(Intercept,log10_body_size)     5595     5115

Regression Coefficients:
                Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept          -1.96      0.42    -2.74    -1.09 1.00     3111     3808
log10_body_size     0.87      0.17     0.52     1.20 1.00     2549     3676

Further Distributional Parameters:
      Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma     0.04      0.02     0.02     0.08 1.00     2226     3234

Draws were sampled using sample(hmc). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).

Phylogenetic signal

hyp <- paste(
  "sd_phylo__Intercept^2 /",
  "(sd_phylo__Intercept^2 + sd_sex__Intercept^2 + sigma^2) = 0"
)
(hyp <- hypothesis(model_phylo_stomach, hyp, class = NULL))

Hypothesis Tests for class :
                Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
1 (sd_phylo__Interc... = 0     0.77      0.26     0.12     0.99       0.02
  Post.Prob Star
1      0.02    *
---
'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
'*': For one-sided hypotheses, the posterior probability exceeds 95%;
for two-sided hypotheses, the value tested against lies outside the 95%-CI.
Posterior probabilities of point hypotheses assume equal prior probabilities.

lambda_stomach <- hyp$hypothesis$Estimate

I will next extract, for each sex, the estimated slope and intercept, together with the 95% credible intervals.

# Extract combined coefficients (fixed + random)
coef(model_phylo_stomach)$sex %>%
{tibble(
  sex = dimnames(.)[[1]],
  intercept    = .[, "Estimate", "Intercept"],
  intercept_low  = .[, "Q2.5", "Intercept"], 
  intercept_high = .[, "Q97.5", "Intercept"]
)} %>%
bind_cols(
  tibble(
    sex = dimnames(coef(model_phylo_stomach)$sex)[[1]],
    slope = coef(model_phylo_stomach)$sex[, "Estimate", "log10_body_size"]
  ) %>% select(slope),
  tibble(
    sex = dimnames(coef(model_phylo_stomach)$sex)[[1]],
    slope_low  = coef(model_phylo_stomach)$sex[, "Q2.5", "log10_body_size"],
    slope_high = coef(model_phylo_stomach)$sex[, "Q97.5", "log10_body_size"]
  ) %>% select(slope_low, slope_high)
)

# A tibble: 2 × 7
  sex    intercept intercept_low intercept_high slope slope_low slope_high
  <chr>      <dbl>         <dbl>          <dbl> <dbl>     <dbl>      <dbl>
1 female     -1.94         -2.63          -1.17 0.872     0.586       1.12
2 male       -1.97         -2.65          -1.21 0.878     0.594       1.13

Model comparison

loo_simple <- loo(model_simple_stomach)
loo_phylo <- loo(model_phylo_stomach)
loo_compare(loo_simple, loo_phylo)

                     elpd_diff se_diff
model_phylo_stomach    0.0       0.0  
model_simple_stomach -23.3       3.6  

In this comparison, the phylogenetic model is clearly preferable to the model treating species as independent observational units. The phylogenetic model (model_phylo_stomach) is used as the reference with elpd_diff = 0, while the simpler model (model_simple_stomach) has an expected log predictive density (ELPD) that is about 23.3 units lower, with an associated standard error of 3.6. In leave-one-out cross-validation, differences exceeding approximately four times their standard error indicate strong evidence. Here, 23.3/3.6≈6.5, providing strong evidence favouring the phylogenetic model..

Lungs

Filter data and prune tree

# Filter organ of interest
dat_organ <- dat_mean %>%
  group_by(organ_grouped, sex) %>%
  ungroup() %>%
  filter(organ_grouped == "lungs")

# Check for database/tree species mismatches
setdiff(tree$tip.label, dat_organ$phylo)      # Tree species absent in database

  [1] "Petrochromis_famula"             "Lobochilotes_labiatus"          
  [3] "Simochromis_diagramma"           "Petrochromis_orthognathus"      
  [5] "Ctenochromis_horei"              "Limnotilapia_dardennii"         
  [7] "Gnathochromis_pfefferi"          "Tropheus_moorii"                
  [9] "Tropheus_brichardi"              "Haplotaxodon_microlepis"        
 [11] "Perissodus_microlepis"           "Benthochromis_tricoti"          
 [13] "Cyprichromis_leptosoma"          "Greenwoodochromis_christyi"     
 [15] "Limnochromis_staneri"            "Gnathochromis_permaxillaris"    
 [17] "Baileychromis_centropomoides"    "Triglachromis_otostigma"        
 [19] "Cyphotilapia_frontosa"           "Ophthalmotilapia_ventralis"     
 [21] "Cyathopharynx_furcifer"          "Ophthalmotilapia_nasuta"        
 [23] "Ophthalmotilapia_boops"          "Aulonocranus_dewindti"          
 [25] "Ectodus_descampsii"              "Callochromis_melanostigma"      
 [27] "Xenotilapia_melanogenys"         "Xenotilapia_flavipinnis"        
 [29] "Eretmodus_cyanostictus"          "Tanganicodus_irsacae"           
 [31] "Spathodus_marlieri"              "Spathodus_erythrodon"           
 [33] "Neolamprologus_brichardi"        "Julidochromis_regani"           
 [35] "Julidochromis_marlieri"          "Neolamprologus_tetracanthus"    
 [37] "Telmatochromis_temporalis"       "Lepidiolamprologus_elongatus"   
 [39] "Lepidiolamprologus_profundicola" "Lepidiolamprologus_nkambae"     
 [41] "Altolamprologus_compressiceps"   "Neolamprologus_brevis"          
 [43] "Chalinochromis_brichardi"        "Julidochromis_ornatus"          
 [45] "Lamprologus_ornatipinnis"        "Neolamprologus_pulcher"         
 [47] "Variabilichromis_moorii"         "Neolamprologus_tretocephalus"   
 [49] "Neolamprologus_sexfasciatus"     "Trematocara_unimaculatum"       
 [51] "Hemibates_stenosoma"             "Bathybates_ferox"               
 [53] "Oreochromis_niloticus"           "Poecilia_reticulata"            
 [55] "Nerophis_lumbriciformis"         "Syngnathus_abaster"             
 [57] "Syngnathus_schlegeli"            "Hippocampus_comes"              
 [59] "Hippocampus_trimaculatus"        "Hippocampus_kuda"               
 [61] "Hippocampus_spinosissimus"       "Hippocampus_abdominalis"        
 [63] "Hippichthys_cyanospilos"         "Syngnathoides_biaculeatus"      
 [65] "Corythoichthys_intestinalis"     "Corythoichthys_haematopterus"   
 [67] "Doryichthys_boaja"               "Doryrhamphus_japonicus"         
 [69] "Entelurus_aequoreus"             "Anguilla_anguilla"              
 [71] "Syncerus_caffer"                 "Tragelaphus_eurycerus"          
 [73] "Tragelaphus_scriptus"            "Redunca_arundinum"              
 [75] "Antidorcas_marsupialis"          "Nanger_granti"                  
 [77] "Raphicerus_campestris"           "Cephalophus_natalensis"         
 [79] "Sylvicapra_grimmia"              "Oreotragus_oreotragus"          
 [81] "Hippotragus_equinus"             "Addax_nasomaculatus"            
 [83] "Oryx_gazella"                    "Connochaetes_taurinus"          
 [85] "Damaliscus_lunatus"              "Ovis_aries"                     
 [87] "Aepyceros_melampus"              "Pteropus_alecto"                
 [89] "Pteropus_poliocephalus"          "Pteropus_scapulatus"            
 [91] "Chlorocebus_aethiops"            "Chlorocebus_sabaeus"            
 [93] "Erythrocebus_patas"              "Papio_cynocephalus"             
 [95] "Papio_anubis"                    "Cercocebus_atys"                
 [97] "Macaca_arctoides"                "Macaca_mulatta"                 
 [99] "Macaca_maura"                    "Trachypithecus_francoisi"       
[101] "Platycercus_caledonicus"         "Platycercus_elegans"            
[103] "Platycercus_eximius"             "Platycercus_venustus"           
[105] "Barnardius_zonarius"             "Northiella_haematogaster"       
[107] "Lathamus_discolor"               "Neophema_chrysostoma"           
[109] "Neophema_pulchella"              "Psittacula_krameri"             
[111] "Eclectus_roratus"                "Aprosmictus_jonquillaceus"      
[113] "Alisterus_scapularis"            "Alisterus_amboinensis"          
[115] "Polytelis_alexandrae"            "Trichoglossus_haematodus"       
[117] "Agapornis_lilianae"              "Agapornis_taranta"              
[119] "Loriculus_vernalis"              "Ara_ararauna"                   
[121] "Guaruba_guarouba"                "Enicognathus_leptorhynchus"     
[123] "Pionites_melanocephalus"         "Forpus_coelestis"               
[125] "Forpus_passerinus"               "Amazona_leucocephala"           
[127] "Amazona_albifrons"               "Amazona_pretrei"                
[129] "Amazona_vinacea"                 "Amazona_finschi"                
[131] "Amazona_amazonica"               "Amazona_ochrocephala"           
[133] "Amazona_aestiva"                 "Brotogeris_versicolurus"        
[135] "Brotogeris_pyrrhoptera"          "Bolborhynchus_lineola"          
[137] "Poicephalus_gulielmi"            "Poicephalus_meyeri"             
[139] "Psittacus_erithacus"             "Serinus_mennelli"               
[141] "Ficedula_hypoleuca"              "Padda_oryzivora"                
[143] "Lonchura_punctulata"             "Lonchura_flaviprymna"           
[145] "Lonchura_bicolor"                "Hypargos_niveoguttatus"         
[147] "Pytilia_hypogrammica"            "Uraeginthus_bengalus"           
[149] "Amandava_amandava"               "Plectrophenax_nivalis"          
[151] "Serinus_canaria"                 "Serinus_serinus"                
[153] "Loxia_curvirostra"               "Carduelis_carduelis"            
[155] "Carpodacus_roseus"               "Uragus_sibiricus"               
[157] "Pyrrhula_pyrrhula"               "Pinicola_enucleator"            
[159] "Bucanetes_githagineus"           "Coccothraustes_coccothraustes"  
[161] "Mycerobas_affinis"               "Mycerobas_carnipes"             
[163] "Fringilla_montifringilla"        "Fringilla_coelebs"              
[165] "Anas_platyrhynchos"              "Anas_acuta"                     
[167] "Anas_crecca"                     "Mergus_serrator"                
[169] "Mergus_merganser"                "Bucephala_clangula"             
[171] "Melanitta_nigra"                 "Somateria_mollissima"           
[173] "Callonetta_leucophrys"           "Branta_bernicla"                
[175] "Branta_leucopsis"                "Anser_anser"                    
[177] "Cygnus_columbianus"              "Tadorna_tadorna"                
[179] "Coturnix_japonica"               "Pucrasia_macrolopha"            
[181] "Phasianus_colchicus"             "Chrysolophus_pictus"            
[183] "Lophura_nycthemera"              "Lophura_ignita"                 
[185] "Syrmaticus_ellioti"              "Syrmaticus_reevesii"            
[187] "Perdix_perdix"                   "Tetrao_urogallus"               
[189] "Lagopus_muta"                    "Lagopus_lagopus"                
[191] "Lophophorus_impejanus"           "Tragopan_temminckii"            
[193] "Pavo_cristatus"                  "Gallus_gallus"                  
[195] "Gallus_sonneratii"               "Rollulus_rouloul"               
[197] "Arborophila_torqueola"           "Numida_meleagris"               

setdiff(dat_organ$phylo, tree$tip.label)      # Database species absent in tree

character(0)

# Exclude mismatched species for consistency
tree_organ <- keep.tip(tree, intersect(tree$tip.label, dat_organ$phylo))
dat_organ <- dat_organ[dat_organ$phylo %in% tree_organ$tip.label, ]

# Re-check for mismatches after pruning
setdiff(tree_organ$tip.label, dat_organ$phylo)

character(0)

setdiff(dat_organ$phylo, tree_organ$tip.label)

character(0)

# Is ultrametric?
is.ultrametric(tree_organ)

[1] TRUE

# how many species?
length(tree_organ$tip.label)

[1] 6

# Compute phylogenetic covariance matrix
A_organ <- ape::vcv.phylo(tree_organ, corr = TRUE)

Model simple

model_simple_lungs <- brm(
  log10_organ_size ~ 
    1 + 
    log10_body_size +
    (1 + log10_body_size | sex),
  data = dat_organ,
  family = gaussian(),
    prior = c(
    prior(normal(0.75, 0.5), class = "b", coef = "log10_body_size"),
    prior(normal(0, 2), class = "Intercept"),
    prior(student_t(3, 0, 0.5), class = "sd"),
    prior(student_t(3, 0, 1),   class = "sigma")
  ),
  seed = 6955,
  sample_prior = TRUE, 
  chains = 4, 
  cores = 4, 
  threads = threading(2),
  iter = 4000, 
  warmup = 2000,
  control = list(max_treedepth = 15,
                 adapt_delta = 0.99),
  save_pars = save_pars(all = TRUE),
  silent = TRUE, refresh = 0
)

Running MCMC with 4 parallel chains, with 2 thread(s) per chain...

Chain 1 finished in 1.9 seconds.
Chain 4 finished in 1.7 seconds.
Chain 3 finished in 2.0 seconds.
Chain 2 finished in 2.3 seconds.

All 4 chains finished successfully.
Mean chain execution time: 2.0 seconds.
Total execution time: 2.3 seconds.

Model check

pp_check(model_simple_lungs)

Model summary

summary(model_simple_lungs)

 Family: gaussian 
  Links: mu = identity; sigma = identity 
Formula: log10_organ_size ~ 1 + log10_body_size + (1 + log10_body_size | sex) 
   Data: dat_organ (Number of observations: 12) 
  Draws: 4 chains, each with iter = 4000; warmup = 2000; thin = 1;
         total post-warmup draws = 8000

Multilevel Hyperparameters:
~sex (Number of levels: 2) 
                               Estimate Est.Error l-95% CI u-95% CI Rhat
sd(Intercept)                      0.31      0.33     0.01     1.16 1.00
sd(log10_body_size)                0.21      0.23     0.00     0.81 1.00
cor(Intercept,log10_body_size)    -0.08      0.60    -0.97     0.94 1.00
                               Bulk_ESS Tail_ESS
sd(Intercept)                      3402     3559
sd(log10_body_size)                2134     2245
cor(Intercept,log10_body_size)     3557     4522

Regression Coefficients:
                Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept          -2.52      0.36    -3.22    -1.75 1.00     4350     4283
log10_body_size     1.05      0.19     0.60     1.38 1.00     2581     2303

Further Distributional Parameters:
      Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma     0.27      0.08     0.17     0.46 1.00     4371     4081

Draws were sampled using sample(hmc). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).

I will next extract, for each sex, the estimated slope and intercept, together with the 95% credible intervals.

# Extract combined coefficients (fixed + random)
coef(model_simple_lungs)$sex %>%
{tibble(
  sex = dimnames(.)[[1]],
  intercept    = .[, "Estimate", "Intercept"],
  intercept_low  = .[, "Q2.5", "Intercept"], 
  intercept_high = .[, "Q97.5", "Intercept"]
)} %>%
bind_cols(
  tibble(
    sex = dimnames(coef(model_simple_lungs)$sex)[[1]],
    slope = coef(model_simple_lungs)$sex[, "Estimate", "log10_body_size"]
  ) %>% select(slope),
  tibble(
    sex = dimnames(coef(model_simple_lungs)$sex)[[1]],
    slope_low  = coef(model_simple_lungs)$sex[, "Q2.5", "log10_body_size"],
    slope_high = coef(model_simple_lungs)$sex[, "Q97.5", "log10_body_size"]
  ) %>% select(slope_low, slope_high)
)

# A tibble: 2 × 7
  sex    intercept intercept_low intercept_high slope slope_low slope_high
  <chr>      <dbl>         <dbl>          <dbl> <dbl>     <dbl>      <dbl>
1 female     -2.54         -3.04          -2.03  1.10     0.858       1.33
2 male       -2.52         -3.01          -2.00  1.07     0.838       1.28

Model with phylogeny

model_phylo_lungs <- brm(
  log10_organ_size ~ 
    1 + 
    log10_body_size +
    (1 + log10_body_size | sex) +
    (1 | gr(phylo, cov = A_organ)),
  data = dat_organ,
  data2 = list(A_organ = A_organ),
  family = gaussian(),
    prior = c(
    prior(normal(0.75, 0.5), class = "b", coef = "log10_body_size"),
    prior(normal(0, 2), class = "Intercept"),
    prior(student_t(3, 0, 0.5), class = "sd"),
    prior(student_t(3, 0, 1),   class = "sigma")
  ),
  seed = 6955,
  sample_prior = TRUE, 
  chains = 4, 
  cores = 4, 
  threads = threading(2),
  iter = 4000, 
  warmup = 2000,
  control = list(max_treedepth = 15,
                 adapt_delta = 0.99),
  save_pars = save_pars(all = TRUE),
  silent = TRUE, refresh = 0
)

Running MCMC with 4 parallel chains, with 2 thread(s) per chain...

Chain 1 finished in 9.9 seconds.
Chain 2 finished in 11.0 seconds.
Chain 3 finished in 13.1 seconds.
Chain 4 finished in 13.0 seconds.

All 4 chains finished successfully.
Mean chain execution time: 11.7 seconds.
Total execution time: 13.3 seconds.

Model check

pp_check(model_phylo_lungs)

Model summary

summary(model_phylo_lungs)

 Family: gaussian 
  Links: mu = identity; sigma = identity 
Formula: log10_organ_size ~ 1 + log10_body_size + (1 + log10_body_size | sex) + (1 | gr(phylo, cov = A_organ)) 
   Data: dat_organ (Number of observations: 12) 
  Draws: 4 chains, each with iter = 4000; warmup = 2000; thin = 1;
         total post-warmup draws = 8000

Multilevel Hyperparameters:
~phylo (Number of levels: 6) 
              Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept)     0.47      0.23     0.18     1.07 1.00     1790     3470

~sex (Number of levels: 2) 
                               Estimate Est.Error l-95% CI u-95% CI Rhat
sd(Intercept)                      0.29      0.30     0.01     1.10 1.00
sd(log10_body_size)                0.21      0.23     0.01     0.81 1.00
cor(Intercept,log10_body_size)    -0.12      0.59    -0.98     0.93 1.00
                               Bulk_ESS Tail_ESS
sd(Intercept)                      2725     2891
sd(log10_body_size)                2128     2871
cor(Intercept,log10_body_size)     5703     4758

Regression Coefficients:
                Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept          -2.39      0.53    -3.37    -1.23 1.00     3691     3976
log10_body_size     0.93      0.20     0.49     1.31 1.00     3113     3672

Further Distributional Parameters:
      Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma     0.08      0.04     0.03     0.17 1.00     1198     3053

Draws were sampled using sample(hmc). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).

Phylogenetic signal

hyp <- paste(
  "sd_phylo__Intercept^2 /",
  "(sd_phylo__Intercept^2 + sd_sex__Intercept^2 + sigma^2) = 0"
)
(hyp <- hypothesis(model_phylo_lungs, hyp, class = NULL))

Hypothesis Tests for class :
                Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
1 (sd_phylo__Interc... = 0     0.69      0.28     0.08     0.99       0.04
  Post.Prob Star
1      0.04    *
---
'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
'*': For one-sided hypotheses, the posterior probability exceeds 95%;
for two-sided hypotheses, the value tested against lies outside the 95%-CI.
Posterior probabilities of point hypotheses assume equal prior probabilities.

lambda_lungs <- hyp$hypothesis$Estimate

I will next extract, for each sex, the estimated slope and intercept, together with the 95% credible intervals.

# Extract combined coefficients (fixed + random)
coef(model_phylo_lungs)$sex %>%
{tibble(
  sex = dimnames(.)[[1]],
  intercept    = .[, "Estimate", "Intercept"],
  intercept_low  = .[, "Q2.5", "Intercept"], 
  intercept_high = .[, "Q97.5", "Intercept"]
)} %>%
bind_cols(
  tibble(
    sex = dimnames(coef(model_phylo_lungs)$sex)[[1]],
    slope = coef(model_phylo_lungs)$sex[, "Estimate", "log10_body_size"]
  ) %>% select(slope),
  tibble(
    sex = dimnames(coef(model_phylo_lungs)$sex)[[1]],
    slope_low  = coef(model_phylo_lungs)$sex[, "Q2.5", "log10_body_size"],
    slope_high = coef(model_phylo_lungs)$sex[, "Q97.5", "log10_body_size"]
  ) %>% select(slope_low, slope_high)
)

# A tibble: 2 × 7
  sex    intercept intercept_low intercept_high slope slope_low slope_high
  <chr>      <dbl>         <dbl>          <dbl> <dbl>     <dbl>      <dbl>
1 female     -2.45         -3.28          -1.39 0.978     0.647       1.23
2 male       -2.35         -3.19          -1.33 0.919     0.614       1.15

Model comparison

loo_simple <- loo(model_simple_lungs)
loo_phylo <- loo(model_phylo_lungs)
loo_compare(loo_simple, loo_phylo)

                   elpd_diff se_diff
model_phylo_lungs    0.0       0.0  
model_simple_lungs -12.7       1.4  

In this comparison, the model that accounts for phylogeny is clearly preferable to the model that treats species as independent observational units. The phylogenetic model (model_phylo_lungs) is used as the reference with elpd_diff = 0, while the simpler model (model_simple_lungs) has an expected log predictive density (ELPD) that is about 12.7 units lower, with an associated standard error of 1.4. In the context of leave‑one‑out cross‑validation, differences exceeding roughly four times their standard error are typically regarded as strong evidence. Here, 12.7/1.4≈9.1, indicating a very large difference relative to its uncertainty, and thus providing strong support for the phylogenetic model.

Adrenal glands

Filter data and prune tree

# Filter organ of interest
dat_organ <- dat_mean %>%
  group_by(organ_grouped, sex) %>%
  ungroup() %>%
  filter(organ_grouped == "adrenal glands")

# Check for database/tree species mismatches
setdiff(tree$tip.label, dat_organ$phylo)      # Tree species absent in database

  [1] "Petrochromis_famula"             "Lobochilotes_labiatus"          
  [3] "Simochromis_diagramma"           "Petrochromis_orthognathus"      
  [5] "Ctenochromis_horei"              "Limnotilapia_dardennii"         
  [7] "Gnathochromis_pfefferi"          "Tropheus_moorii"                
  [9] "Tropheus_brichardi"              "Haplotaxodon_microlepis"        
 [11] "Perissodus_microlepis"           "Benthochromis_tricoti"          
 [13] "Cyprichromis_leptosoma"          "Greenwoodochromis_christyi"     
 [15] "Limnochromis_staneri"            "Gnathochromis_permaxillaris"    
 [17] "Baileychromis_centropomoides"    "Triglachromis_otostigma"        
 [19] "Cyphotilapia_frontosa"           "Ophthalmotilapia_ventralis"     
 [21] "Cyathopharynx_furcifer"          "Ophthalmotilapia_nasuta"        
 [23] "Ophthalmotilapia_boops"          "Aulonocranus_dewindti"          
 [25] "Ectodus_descampsii"              "Callochromis_melanostigma"      
 [27] "Xenotilapia_melanogenys"         "Xenotilapia_flavipinnis"        
 [29] "Eretmodus_cyanostictus"          "Tanganicodus_irsacae"           
 [31] "Spathodus_marlieri"              "Spathodus_erythrodon"           
 [33] "Neolamprologus_brichardi"        "Julidochromis_regani"           
 [35] "Julidochromis_marlieri"          "Neolamprologus_tetracanthus"    
 [37] "Telmatochromis_temporalis"       "Lepidiolamprologus_elongatus"   
 [39] "Lepidiolamprologus_profundicola" "Lepidiolamprologus_nkambae"     
 [41] "Altolamprologus_compressiceps"   "Neolamprologus_brevis"          
 [43] "Chalinochromis_brichardi"        "Julidochromis_ornatus"          
 [45] "Lamprologus_ornatipinnis"        "Neolamprologus_pulcher"         
 [47] "Variabilichromis_moorii"         "Neolamprologus_tretocephalus"   
 [49] "Neolamprologus_sexfasciatus"     "Trematocara_unimaculatum"       
 [51] "Hemibates_stenosoma"             "Bathybates_ferox"               
 [53] "Oreochromis_niloticus"           "Poecilia_reticulata"            
 [55] "Nerophis_lumbriciformis"         "Syngnathus_abaster"             
 [57] "Syngnathus_schlegeli"            "Hippocampus_comes"              
 [59] "Hippocampus_trimaculatus"        "Hippocampus_kuda"               
 [61] "Hippocampus_spinosissimus"       "Hippocampus_abdominalis"        
 [63] "Hippichthys_cyanospilos"         "Syngnathoides_biaculeatus"      
 [65] "Corythoichthys_intestinalis"     "Corythoichthys_haematopterus"   
 [67] "Doryichthys_boaja"               "Doryrhamphus_japonicus"         
 [69] "Entelurus_aequoreus"             "Anguilla_anguilla"              
 [71] "Syncerus_caffer"                 "Tragelaphus_eurycerus"          
 [73] "Tragelaphus_scriptus"            "Redunca_arundinum"              
 [75] "Antidorcas_marsupialis"          "Nanger_granti"                  
 [77] "Raphicerus_campestris"           "Cephalophus_natalensis"         
 [79] "Sylvicapra_grimmia"              "Oreotragus_oreotragus"          
 [81] "Hippotragus_equinus"             "Addax_nasomaculatus"            
 [83] "Oryx_gazella"                    "Connochaetes_taurinus"          
 [85] "Damaliscus_lunatus"              "Ovis_aries"                     
 [87] "Aepyceros_melampus"              "Pteropus_alecto"                
 [89] "Pteropus_poliocephalus"          "Pteropus_scapulatus"            
 [91] "Lasiopodomys_brandtii"           "Meriones_unguiculatus"          
 [93] "Chlorocebus_aethiops"            "Chlorocebus_sabaeus"            
 [95] "Erythrocebus_patas"              "Papio_cynocephalus"             
 [97] "Papio_anubis"                    "Cercocebus_atys"                
 [99] "Macaca_arctoides"                "Macaca_mulatta"                 
[101] "Macaca_maura"                    "Trachypithecus_francoisi"       
[103] "Phrynocephalus_vlangalii"        "Platycercus_caledonicus"        
[105] "Platycercus_elegans"             "Platycercus_eximius"            
[107] "Platycercus_venustus"            "Barnardius_zonarius"            
[109] "Northiella_haematogaster"        "Lathamus_discolor"              
[111] "Neophema_chrysostoma"            "Neophema_pulchella"             
[113] "Psittacula_krameri"              "Eclectus_roratus"               
[115] "Aprosmictus_jonquillaceus"       "Alisterus_scapularis"           
[117] "Alisterus_amboinensis"           "Polytelis_alexandrae"           
[119] "Trichoglossus_haematodus"        "Agapornis_lilianae"             
[121] "Agapornis_taranta"               "Loriculus_vernalis"             
[123] "Ara_ararauna"                    "Guaruba_guarouba"               
[125] "Enicognathus_leptorhynchus"      "Pionites_melanocephalus"        
[127] "Forpus_coelestis"                "Forpus_passerinus"              
[129] "Amazona_leucocephala"            "Amazona_albifrons"              
[131] "Amazona_pretrei"                 "Amazona_vinacea"                
[133] "Amazona_finschi"                 "Amazona_amazonica"              
[135] "Amazona_ochrocephala"            "Amazona_aestiva"                
[137] "Brotogeris_versicolurus"         "Brotogeris_pyrrhoptera"         
[139] "Bolborhynchus_lineola"           "Poicephalus_gulielmi"           
[141] "Poicephalus_meyeri"              "Psittacus_erithacus"            
[143] "Serinus_mennelli"                "Ficedula_hypoleuca"             
[145] "Padda_oryzivora"                 "Lonchura_punctulata"            
[147] "Lonchura_flaviprymna"            "Lonchura_bicolor"               
[149] "Hypargos_niveoguttatus"          "Pytilia_hypogrammica"           
[151] "Uraeginthus_bengalus"            "Amandava_amandava"              
[153] "Plectrophenax_nivalis"           "Serinus_canaria"                
[155] "Serinus_serinus"                 "Loxia_curvirostra"              
[157] "Carduelis_carduelis"             "Carpodacus_roseus"              
[159] "Uragus_sibiricus"                "Pyrrhula_pyrrhula"              
[161] "Pinicola_enucleator"             "Bucanetes_githagineus"          
[163] "Coccothraustes_coccothraustes"   "Mycerobas_affinis"              
[165] "Mycerobas_carnipes"              "Fringilla_montifringilla"       
[167] "Fringilla_coelebs"               "Anas_acuta"                     
[169] "Anas_crecca"                     "Mergus_serrator"                
[171] "Mergus_merganser"                "Bucephala_clangula"             
[173] "Melanitta_nigra"                 "Somateria_mollissima"           
[175] "Callonetta_leucophrys"           "Branta_bernicla"                
[177] "Branta_leucopsis"                "Anser_anser"                    
[179] "Cygnus_columbianus"              "Tadorna_tadorna"                
[181] "Pucrasia_macrolopha"             "Phasianus_colchicus"            
[183] "Chrysolophus_pictus"             "Lophura_nycthemera"             
[185] "Lophura_ignita"                  "Syrmaticus_ellioti"             
[187] "Syrmaticus_reevesii"             "Perdix_perdix"                  
[189] "Tetrao_urogallus"                "Lagopus_muta"                   
[191] "Lagopus_lagopus"                 "Lophophorus_impejanus"          
[193] "Tragopan_temminckii"             "Pavo_cristatus"                 
[195] "Gallus_gallus"                   "Gallus_sonneratii"              
[197] "Rollulus_rouloul"                "Arborophila_torqueola"          
[199] "Numida_meleagris"               

setdiff(dat_organ$phylo, tree$tip.label)      # Database species absent in tree

character(0)

# Exclude mismatched species for consistency
tree_organ <- keep.tip(tree, intersect(tree$tip.label, dat_organ$phylo))
dat_organ <- dat_organ[dat_organ$phylo %in% tree_organ$tip.label, ]

# Re-check for mismatches after pruning
setdiff(tree_organ$tip.label, dat_organ$phylo)

character(0)

setdiff(dat_organ$phylo, tree_organ$tip.label)

character(0)

# Is ultrametric?
is.ultrametric(tree_organ)

[1] TRUE

# how many species?
length(tree_organ$tip.label)

[1] 5

# Compute phylogenetic covariance matrix
A_organ <- ape::vcv.phylo(tree_organ, corr = TRUE)

Model simple

model_simple_adrenal_glands <- brm(
  log10_organ_size ~ 
    1 + 
    log10_body_size +
    (1 + log10_body_size | sex),
  data = dat_organ,
  family = gaussian(),
    prior = c(
    prior(normal(0.75, 0.5), class = "b", coef = "log10_body_size"),
    prior(normal(0, 2), class = "Intercept"),
    prior(student_t(3, 0, 0.5), class = "sd"),
    prior(student_t(3, 0, 1),   class = "sigma")
  ),
  seed = 6955,
  sample_prior = TRUE, 
  chains = 4, 
  cores = 4, 
  threads = threading(2),
  iter = 4000, 
  warmup = 2000,
  control = list(max_treedepth = 15,
                 adapt_delta = 0.99),
  save_pars = save_pars(all = TRUE),
  silent = TRUE, refresh = 0
)

Running MCMC with 4 parallel chains, with 2 thread(s) per chain...

Chain 4 finished in 1.5 seconds.
Chain 1 finished in 1.7 seconds.
Chain 2 finished in 1.9 seconds.
Chain 3 finished in 1.8 seconds.

All 4 chains finished successfully.
Mean chain execution time: 1.7 seconds.
Total execution time: 2.1 seconds.

Model check

pp_check(model_simple_adrenal_glands)

Model summary

summary(model_simple_adrenal_glands)

 Family: gaussian 
  Links: mu = identity; sigma = identity 
Formula: log10_organ_size ~ 1 + log10_body_size + (1 + log10_body_size | sex) 
   Data: dat_organ (Number of observations: 10) 
  Draws: 4 chains, each with iter = 4000; warmup = 2000; thin = 1;
         total post-warmup draws = 8000

Multilevel Hyperparameters:
~sex (Number of levels: 2) 
                               Estimate Est.Error l-95% CI u-95% CI Rhat
sd(Intercept)                      0.32      0.33     0.01     1.18 1.00
sd(log10_body_size)                0.20      0.22     0.01     0.80 1.00
cor(Intercept,log10_body_size)    -0.11      0.59    -0.98     0.94 1.00
                               Bulk_ESS Tail_ESS
sd(Intercept)                      3565     2537
sd(log10_body_size)                2615     3544
cor(Intercept,log10_body_size)     3227     3452

Regression Coefficients:
                Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept          -3.00      0.37    -3.72    -2.24 1.00     4586     4119
log10_body_size     0.74      0.17     0.41     1.11 1.00     2893     2630

Further Distributional Parameters:
      Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma     0.26      0.09     0.15     0.48 1.00     3971     3995

Draws were sampled using sample(hmc). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).

I will next extract, for each sex, the estimated slope and intercept, together with the 95% credible intervals.

# Extract combined coefficients (fixed + random)
coef(model_simple_adrenal_glands)$sex %>%
{tibble(
  sex = dimnames(.)[[1]],
  intercept    = .[, "Estimate", "Intercept"],
  intercept_low  = .[, "Q2.5", "Intercept"], 
  intercept_high = .[, "Q97.5", "Intercept"]
)} %>%
bind_cols(
  tibble(
    sex = dimnames(coef(model_simple_adrenal_glands)$sex)[[1]],
    slope = coef(model_simple_adrenal_glands)$sex[, "Estimate", "log10_body_size"]
  ) %>% select(slope),
  tibble(
    sex = dimnames(coef(model_simple_adrenal_glands)$sex)[[1]],
    slope_low  = coef(model_simple_adrenal_glands)$sex[, "Q2.5", "log10_body_size"],
    slope_high = coef(model_simple_adrenal_glands)$sex[, "Q97.5", "log10_body_size"]
  ) %>% select(slope_low, slope_high)
)

# A tibble: 2 × 7
  sex    intercept intercept_low intercept_high slope slope_low slope_high
  <chr>      <dbl>         <dbl>          <dbl> <dbl>     <dbl>      <dbl>
1 female     -2.99         -3.54          -2.44 0.720     0.508      0.926
2 male       -3.05         -3.59          -2.50 0.727     0.520      0.932

Model with phylogeny

model_phylo_adrenal_glands <- brm(
  log10_organ_size ~ 
    1 + 
    log10_body_size +
    (1 + log10_body_size | sex) +
    (1 | gr(phylo, cov = A_organ)),
  data = dat_organ,
  data2 = list(A_organ = A_organ),
  family = gaussian(),
    prior = c(
    prior(normal(0.75, 0.5), class = "b", coef = "log10_body_size"),
    prior(normal(0, 2), class = "Intercept"),
    prior(student_t(3, 0, 0.5), class = "sd"),
    prior(student_t(3, 0, 1),   class = "sigma")
  ),
  seed = 6955,
  sample_prior = TRUE, 
  chains = 4, 
  cores = 4, 
  threads = threading(2),
  iter = 4000, 
  warmup = 2000,
  control = list(max_treedepth = 15,
                 adapt_delta = 0.99),
  save_pars = save_pars(all = TRUE),
  silent = TRUE, refresh = 0
)

Running MCMC with 4 parallel chains, with 2 thread(s) per chain...

Chain 2 finished in 3.5 seconds.
Chain 3 finished in 3.9 seconds.
Chain 1 finished in 4.0 seconds.
Chain 4 finished in 4.0 seconds.

All 4 chains finished successfully.
Mean chain execution time: 3.9 seconds.
Total execution time: 4.2 seconds.

Model checks

pp_check(model_phylo_adrenal_glands)

Model summary

summary(model_phylo_adrenal_glands)

 Family: gaussian 
  Links: mu = identity; sigma = identity 
Formula: log10_organ_size ~ 1 + log10_body_size + (1 + log10_body_size | sex) + (1 | gr(phylo, cov = A_organ)) 
   Data: dat_organ (Number of observations: 10) 
  Draws: 4 chains, each with iter = 4000; warmup = 2000; thin = 1;
         total post-warmup draws = 8000

Multilevel Hyperparameters:
~phylo (Number of levels: 5) 
              Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept)     0.35      0.23     0.02     0.92 1.00     2085     2237

~sex (Number of levels: 2) 
                               Estimate Est.Error l-95% CI u-95% CI Rhat
sd(Intercept)                      0.31      0.32     0.01     1.14 1.00
sd(log10_body_size)                0.19      0.22     0.00     0.80 1.00
cor(Intercept,log10_body_size)    -0.09      0.60    -0.97     0.95 1.00
                               Bulk_ESS Tail_ESS
sd(Intercept)                      4236     3612
sd(log10_body_size)                2443     4133
cor(Intercept,log10_body_size)     5135     4652

Regression Coefficients:
                Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept          -3.05      0.47    -4.01    -2.06 1.00     4480     4249
log10_body_size     0.76      0.18     0.41     1.16 1.00     2808     2514

Further Distributional Parameters:
      Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma     0.18      0.09     0.08     0.39 1.00     2083     3940

Draws were sampled using sample(hmc). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).

Phylogenetic signal

hyp <- paste(
  "sd_phylo__Intercept^2 /",
  "(sd_phylo__Intercept^2 + sd_sex__Intercept^2 + sigma^2) = 0"
)
(hyp <- hypothesis(model_phylo_adrenal_glands, hyp, class = NULL))

Hypothesis Tests for class :
                Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
1 (sd_phylo__Interc... = 0     0.47      0.32        0     0.96       0.32
  Post.Prob Star
1      0.24    *
---
'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
'*': For one-sided hypotheses, the posterior probability exceeds 95%;
for two-sided hypotheses, the value tested against lies outside the 95%-CI.
Posterior probabilities of point hypotheses assume equal prior probabilities.

lambda_adrenal_glands <- hyp$hypothesis$Estimate

I will next extract, for each sex, the estimated slope and intercept, together with the 95% credible intervals.

# Extract combined coefficients (fixed + random)
coef(model_phylo_adrenal_glands)$sex %>%
{tibble(
  sex = dimnames(.)[[1]],
  intercept    = .[, "Estimate", "Intercept"],
  intercept_low  = .[, "Q2.5", "Intercept"], 
  intercept_high = .[, "Q97.5", "Intercept"]
)} %>%
bind_cols(
  tibble(
    sex = dimnames(coef(model_phylo_adrenal_glands)$sex)[[1]],
    slope = coef(model_phylo_adrenal_glands)$sex[, "Estimate", "log10_body_size"]
  ) %>% select(slope),
  tibble(
    sex = dimnames(coef(model_phylo_adrenal_glands)$sex)[[1]],
    slope_low  = coef(model_phylo_adrenal_glands)$sex[, "Q2.5", "log10_body_size"],
    slope_high = coef(model_phylo_adrenal_glands)$sex[, "Q97.5", "log10_body_size"]
  ) %>% select(slope_low, slope_high)
)

# A tibble: 2 × 7
  sex    intercept intercept_low intercept_high slope slope_low slope_high
  <chr>      <dbl>         <dbl>          <dbl> <dbl>     <dbl>      <dbl>
1 female     -3.03         -3.84          -2.22 0.743     0.519      0.968
2 male       -3.11         -3.91          -2.32 0.755     0.537      0.976

Model comparison

loo_simple <- loo(model_simple_adrenal_glands)
loo_phylo <- loo(model_phylo_adrenal_glands)
loo_compare(loo_simple, loo_phylo)

                            elpd_diff se_diff
model_phylo_adrenal_glands   0.0       0.0   
model_simple_adrenal_glands -2.6       0.7   

In this comparison, the model that accounts for phylogeny is clearly preferable to the model that treats species as independent observational units. The phylogenetic model (model_phylo_adrenal glands) is used as the reference with elpd_diff = 0, whereas the simpler model (model_simple_adrenal glands) has an expected log predictive density (ELPD) that is about 2.6 units lower, with an associated standard error of 0.7 In the context of leave‑one‑out cross‑validation, differences exceeding roughly four times their standard error are typically regarded as strong evidence. Here, 2.6/0.7≈3.7, indicating both models are similarly good.

Kidneys

Filter data and prune tree

# Filter organ of interest
dat_organ <- dat_mean %>%
  group_by(organ_grouped, sex) %>%
  ungroup() %>%
  filter(organ_grouped == "kidneys")

# Check for database/tree species mismatches
setdiff(tree$tip.label, dat_organ$phylo)      # Tree species absent in database

  [1] "Petrochromis_famula"             "Lobochilotes_labiatus"          
  [3] "Simochromis_diagramma"           "Petrochromis_orthognathus"      
  [5] "Ctenochromis_horei"              "Limnotilapia_dardennii"         
  [7] "Gnathochromis_pfefferi"          "Tropheus_moorii"                
  [9] "Tropheus_brichardi"              "Haplotaxodon_microlepis"        
 [11] "Perissodus_microlepis"           "Benthochromis_tricoti"          
 [13] "Cyprichromis_leptosoma"          "Greenwoodochromis_christyi"     
 [15] "Limnochromis_staneri"            "Gnathochromis_permaxillaris"    
 [17] "Baileychromis_centropomoides"    "Triglachromis_otostigma"        
 [19] "Cyphotilapia_frontosa"           "Ophthalmotilapia_ventralis"     
 [21] "Cyathopharynx_furcifer"          "Ophthalmotilapia_nasuta"        
 [23] "Ophthalmotilapia_boops"          "Aulonocranus_dewindti"          
 [25] "Ectodus_descampsii"              "Callochromis_melanostigma"      
 [27] "Xenotilapia_melanogenys"         "Xenotilapia_flavipinnis"        
 [29] "Eretmodus_cyanostictus"          "Tanganicodus_irsacae"           
 [31] "Spathodus_marlieri"              "Spathodus_erythrodon"           
 [33] "Neolamprologus_brichardi"        "Julidochromis_regani"           
 [35] "Julidochromis_marlieri"          "Neolamprologus_tetracanthus"    
 [37] "Telmatochromis_temporalis"       "Lepidiolamprologus_elongatus"   
 [39] "Lepidiolamprologus_profundicola" "Lepidiolamprologus_nkambae"     
 [41] "Altolamprologus_compressiceps"   "Neolamprologus_brevis"          
 [43] "Chalinochromis_brichardi"        "Julidochromis_ornatus"          
 [45] "Lamprologus_ornatipinnis"        "Neolamprologus_pulcher"         
 [47] "Variabilichromis_moorii"         "Neolamprologus_tretocephalus"   
 [49] "Neolamprologus_sexfasciatus"     "Trematocara_unimaculatum"       
 [51] "Hemibates_stenosoma"             "Bathybates_ferox"               
 [53] "Oreochromis_niloticus"           "Poecilia_reticulata"            
 [55] "Nerophis_lumbriciformis"         "Syngnathus_abaster"             
 [57] "Syngnathus_schlegeli"            "Hippocampus_comes"              
 [59] "Hippocampus_trimaculatus"        "Hippocampus_kuda"               
 [61] "Hippocampus_spinosissimus"       "Hippocampus_abdominalis"        
 [63] "Hippichthys_cyanospilos"         "Syngnathoides_biaculeatus"      
 [65] "Corythoichthys_intestinalis"     "Corythoichthys_haematopterus"   
 [67] "Doryichthys_boaja"               "Doryrhamphus_japonicus"         
 [69] "Entelurus_aequoreus"             "Anguilla_anguilla"              
 [71] "Syncerus_caffer"                 "Tragelaphus_eurycerus"          
 [73] "Tragelaphus_scriptus"            "Redunca_arundinum"              
 [75] "Antidorcas_marsupialis"          "Nanger_granti"                  
 [77] "Raphicerus_campestris"           "Cephalophus_natalensis"         
 [79] "Sylvicapra_grimmia"              "Oreotragus_oreotragus"          
 [81] "Hippotragus_equinus"             "Addax_nasomaculatus"            
 [83] "Oryx_gazella"                    "Connochaetes_taurinus"          
 [85] "Damaliscus_lunatus"              "Ovis_aries"                     
 [87] "Aepyceros_melampus"              "Pteropus_alecto"                
 [89] "Pteropus_poliocephalus"          "Pteropus_scapulatus"            
 [91] "Chlorocebus_aethiops"            "Chlorocebus_sabaeus"            
 [93] "Erythrocebus_patas"              "Papio_cynocephalus"             
 [95] "Papio_anubis"                    "Cercocebus_atys"                
 [97] "Macaca_arctoides"                "Macaca_mulatta"                 
 [99] "Macaca_maura"                    "Trachypithecus_francoisi"       
[101] "Phrynocephalus_vlangalii"        "Platycercus_caledonicus"        
[103] "Platycercus_elegans"             "Platycercus_eximius"            
[105] "Platycercus_venustus"            "Barnardius_zonarius"            
[107] "Northiella_haematogaster"        "Lathamus_discolor"              
[109] "Neophema_chrysostoma"            "Neophema_pulchella"             
[111] "Psittacula_krameri"              "Eclectus_roratus"               
[113] "Aprosmictus_jonquillaceus"       "Alisterus_scapularis"           
[115] "Alisterus_amboinensis"           "Polytelis_alexandrae"           
[117] "Trichoglossus_haematodus"        "Agapornis_lilianae"             
[119] "Agapornis_taranta"               "Loriculus_vernalis"             
[121] "Ara_ararauna"                    "Guaruba_guarouba"               
[123] "Enicognathus_leptorhynchus"      "Pionites_melanocephalus"        
[125] "Forpus_coelestis"                "Forpus_passerinus"              
[127] "Amazona_leucocephala"            "Amazona_albifrons"              
[129] "Amazona_pretrei"                 "Amazona_vinacea"                
[131] "Amazona_finschi"                 "Amazona_amazonica"              
[133] "Amazona_ochrocephala"            "Amazona_aestiva"                
[135] "Brotogeris_versicolurus"         "Brotogeris_pyrrhoptera"         
[137] "Bolborhynchus_lineola"           "Poicephalus_gulielmi"           
[139] "Poicephalus_meyeri"              "Psittacus_erithacus"            
[141] "Serinus_mennelli"                "Ficedula_hypoleuca"             
[143] "Padda_oryzivora"                 "Lonchura_punctulata"            
[145] "Lonchura_flaviprymna"            "Lonchura_bicolor"               
[147] "Hypargos_niveoguttatus"          "Pytilia_hypogrammica"           
[149] "Uraeginthus_bengalus"            "Amandava_amandava"              
[151] "Plectrophenax_nivalis"           "Serinus_canaria"                
[153] "Serinus_serinus"                 "Loxia_curvirostra"              
[155] "Carduelis_carduelis"             "Carpodacus_roseus"              
[157] "Uragus_sibiricus"                "Pyrrhula_pyrrhula"              
[159] "Pinicola_enucleator"             "Bucanetes_githagineus"          
[161] "Coccothraustes_coccothraustes"   "Mycerobas_affinis"              
[163] "Mycerobas_carnipes"              "Fringilla_montifringilla"       
[165] "Fringilla_coelebs"               "Anas_acuta"                     
[167] "Anas_crecca"                     "Mergus_serrator"                
[169] "Mergus_merganser"                "Bucephala_clangula"             
[171] "Melanitta_nigra"                 "Somateria_mollissima"           
[173] "Callonetta_leucophrys"           "Branta_bernicla"                
[175] "Branta_leucopsis"                "Anser_anser"                    
[177] "Cygnus_columbianus"              "Tadorna_tadorna"                
[179] "Coturnix_japonica"               "Pucrasia_macrolopha"            
[181] "Phasianus_colchicus"             "Chrysolophus_pictus"            
[183] "Lophura_nycthemera"              "Lophura_ignita"                 
[185] "Syrmaticus_ellioti"              "Syrmaticus_reevesii"            
[187] "Perdix_perdix"                   "Tetrao_urogallus"               
[189] "Lagopus_muta"                    "Lagopus_lagopus"                
[191] "Lophophorus_impejanus"           "Tragopan_temminckii"            
[193] "Pavo_cristatus"                  "Gallus_gallus"                  
[195] "Gallus_sonneratii"               "Rollulus_rouloul"               
[197] "Arborophila_torqueola"           "Numida_meleagris"               

setdiff(dat_organ$phylo, tree$tip.label)      # Database species absent in tree

character(0)

# Exclude mismatched species for consistency
tree_organ <- keep.tip(tree, intersect(tree$tip.label, dat_organ$phylo))
dat_organ <- dat_organ[dat_organ$phylo %in% tree_organ$tip.label, ]

# Re-check for mismatches after pruning
setdiff(tree_organ$tip.label, dat_organ$phylo)

character(0)

setdiff(dat_organ$phylo, tree_organ$tip.label)

character(0)

# Is ultrametric?
is.ultrametric(tree_organ)

[1] TRUE

# how many species?
length(tree_organ$tip.label)

[1] 6

# Compute phylogenetic covariance matrix
A_organ <- ape::vcv.phylo(tree_organ, corr = TRUE)

Model simple

model_simple_kidneys <- brm(
  log10_organ_size ~ 
    1 + 
    log10_body_size +
    (1 + log10_body_size | sex),
  data = dat_organ,
  family = gaussian(),
    prior = c(
    prior(normal(0.75, 0.5), class = "b", coef = "log10_body_size"),
    prior(normal(0, 2), class = "Intercept"),
    prior(student_t(3, 0, 0.5), class = "sd"),
    prior(student_t(3, 0, 1),   class = "sigma")
  ),
  seed = 6955,
  sample_prior = TRUE, 
  chains = 4, 
  cores = 4, 
  threads = threading(2),
  iter = 4000, 
  warmup = 2000,
  control = list(max_treedepth = 15,
                 adapt_delta = 0.99),
  save_pars = save_pars(all = TRUE),
  silent = TRUE, refresh = 0
)

Running MCMC with 4 parallel chains, with 2 thread(s) per chain...

Chain 4 finished in 3.6 seconds.
Chain 1 finished in 4.1 seconds.
Chain 2 finished in 6.7 seconds.
Chain 3 finished in 7.4 seconds.

All 4 chains finished successfully.
Mean chain execution time: 5.5 seconds.
Total execution time: 7.5 seconds.

Model checks

pp_check(model_simple_kidneys)

Model summary

summary(model_simple_kidneys)

 Family: gaussian 
  Links: mu = identity; sigma = identity 
Formula: log10_organ_size ~ 1 + log10_body_size + (1 + log10_body_size | sex) 
   Data: dat_organ (Number of observations: 12) 
  Draws: 4 chains, each with iter = 4000; warmup = 2000; thin = 1;
         total post-warmup draws = 8000

Multilevel Hyperparameters:
~sex (Number of levels: 2) 
                               Estimate Est.Error l-95% CI u-95% CI Rhat
sd(Intercept)                      0.25      0.30     0.01     1.06 1.00
sd(log10_body_size)                0.16      0.21     0.00     0.73 1.00
cor(Intercept,log10_body_size)    -0.06      0.61    -0.98     0.95 1.00
                               Bulk_ESS Tail_ESS
sd(Intercept)                      2652     3441
sd(log10_body_size)                2110     3759
cor(Intercept,log10_body_size)     4028     4228

Regression Coefficients:
                Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept          -1.69      0.27    -2.22    -1.15 1.00     3154     3098
log10_body_size     0.82      0.13     0.52     1.11 1.00     1875     1832

Further Distributional Parameters:
      Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma     0.09      0.03     0.06     0.16 1.00     4773     3864

Draws were sampled using sample(hmc). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).

I will next extract, for each sex, the estimated slope and intercept, together with the 95% credible intervals.

# Extract combined coefficients (fixed + random)
coef(model_simple_kidneys)$sex %>%
{tibble(
  sex = dimnames(.)[[1]],
  intercept    = .[, "Estimate", "Intercept"],
  intercept_low  = .[, "Q2.5", "Intercept"], 
  intercept_high = .[, "Q97.5", "Intercept"]
)} %>%
bind_cols(
  tibble(
    sex = dimnames(coef(model_simple_kidneys)$sex)[[1]],
    slope = coef(model_simple_kidneys)$sex[, "Estimate", "log10_body_size"]
  ) %>% select(slope),
  tibble(
    sex = dimnames(coef(model_simple_kidneys)$sex)[[1]],
    slope_low  = coef(model_simple_kidneys)$sex[, "Q2.5", "log10_body_size"],
    slope_high = coef(model_simple_kidneys)$sex[, "Q97.5", "log10_body_size"]
  ) %>% select(slope_low, slope_high)
)

# A tibble: 2 × 7
  sex    intercept intercept_low intercept_high slope slope_low slope_high
  <chr>      <dbl>         <dbl>          <dbl> <dbl>     <dbl>      <dbl>
1 female     -1.70         -1.89          -1.52 0.824     0.750      0.903
2 male       -1.68         -1.87          -1.49 0.817     0.744      0.890

Model with phylogeny

model_phylo_kidneys <- brm(
  log10_organ_size ~ 
    1 + 
    log10_body_size +
    (1 + log10_body_size | sex) +
    (1 | gr(phylo, cov = A_organ)),
  data = dat_organ,
  data2 = list(A_organ = A_organ),
  family = gaussian(),
    prior = c(
    prior(normal(0.75, 0.5), class = "b", coef = "log10_body_size"),
    prior(normal(0, 2), class = "Intercept"),
    prior(student_t(3, 0, 0.5), class = "sd"),
    prior(student_t(3, 0, 1),   class = "sigma")
  ),
  seed = 6955,
  sample_prior = TRUE, 
  chains = 4, 
  cores = 4, 
  threads = threading(2),
  iter = 4000, 
  warmup = 2000,
  control = list(max_treedepth = 15,
                 adapt_delta = 0.99),
  save_pars = save_pars(all = TRUE),
  silent = TRUE, refresh = 0
)

Running MCMC with 4 parallel chains, with 2 thread(s) per chain...

Chain 1 finished in 16.0 seconds.
Chain 4 finished in 16.4 seconds.
Chain 3 finished in 20.6 seconds.
Chain 2 finished in 23.0 seconds.

All 4 chains finished successfully.
Mean chain execution time: 19.0 seconds.
Total execution time: 23.1 seconds.

Model checks

pp_check(model_phylo_kidneys)

Model summary

summary(model_phylo_kidneys)

 Family: gaussian 
  Links: mu = identity; sigma = identity 
Formula: log10_organ_size ~ 1 + log10_body_size + (1 + log10_body_size | sex) + (1 | gr(phylo, cov = A_organ)) 
   Data: dat_organ (Number of observations: 12) 
  Draws: 4 chains, each with iter = 4000; warmup = 2000; thin = 1;
         total post-warmup draws = 8000

Multilevel Hyperparameters:
~phylo (Number of levels: 6) 
              Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept)     0.27      0.14     0.07     0.62 1.00     1436     1448

~sex (Number of levels: 2) 
                               Estimate Est.Error l-95% CI u-95% CI Rhat
sd(Intercept)                      0.21      0.26     0.00     0.95 1.00
sd(log10_body_size)                0.12      0.17     0.00     0.60 1.00
cor(Intercept,log10_body_size)    -0.07      0.62    -0.98     0.96 1.00
                               Bulk_ESS Tail_ESS
sd(Intercept)                      3254     3972
sd(log10_body_size)                2187     3539
cor(Intercept,log10_body_size)     5530     4291

Regression Coefficients:
                Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept          -1.52      0.33    -2.20    -0.83 1.00     3327     3840
log10_body_size     0.76      0.12     0.49     1.01 1.00     2975     2672

Further Distributional Parameters:
      Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma     0.03      0.02     0.01     0.09 1.00     1149     1457

Draws were sampled using sample(hmc). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).

Phylogenetic signal

hyp <- paste(
  "sd_phylo__Intercept^2 /",
  "(sd_phylo__Intercept^2 + sd_sex__Intercept^2 + sigma^2) = 0"
)
(hyp <- hypothesis(model_phylo_kidneys, hyp, class = NULL))

Hypothesis Tests for class :
                Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
1 (sd_phylo__Interc... = 0     0.65      0.32     0.03     0.99       0.12
  Post.Prob Star
1      0.11    *
---
'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
'*': For one-sided hypotheses, the posterior probability exceeds 95%;
for two-sided hypotheses, the value tested against lies outside the 95%-CI.
Posterior probabilities of point hypotheses assume equal prior probabilities.

lambda_kidneys <- hyp$hypothesis$Estimate

I will next extract, for each sex, the estimated slope and intercept, together with the 95% credible intervals.

# Extract combined coefficients (fixed + random)
coef(model_phylo_kidneys)$sex %>%
{tibble(
  sex = dimnames(.)[[1]],
  intercept    = .[, "Estimate", "Intercept"],
  intercept_low  = .[, "Q2.5", "Intercept"], 
  intercept_high = .[, "Q97.5", "Intercept"]
)} %>%
bind_cols(
  tibble(
    sex = dimnames(coef(model_phylo_kidneys)$sex)[[1]],
    slope = coef(model_phylo_kidneys)$sex[, "Estimate", "log10_body_size"]
  ) %>% select(slope),
  tibble(
    sex = dimnames(coef(model_phylo_kidneys)$sex)[[1]],
    slope_low  = coef(model_phylo_kidneys)$sex[, "Q2.5", "log10_body_size"],
    slope_high = coef(model_phylo_kidneys)$sex[, "Q97.5", "log10_body_size"]
  ) %>% select(slope_low, slope_high)
)

# A tibble: 2 × 7
  sex    intercept intercept_low intercept_high slope slope_low slope_high
  <chr>      <dbl>         <dbl>          <dbl> <dbl>     <dbl>      <dbl>
1 female     -1.53         -2.06         -0.971 0.773     0.649      0.895
2 male       -1.50         -2.03         -0.946 0.766     0.646      0.880

Model comparison

loo_simple <- loo(model_simple_kidneys)
loo_phylo <- loo(model_phylo_kidneys)
loo_compare(loo_simple, loo_phylo)

                     elpd_diff se_diff
model_phylo_kidneys    0.0       0.0  
model_simple_kidneys -10.3       1.5  

In this comparison, the phylogenetic model is clearly preferable to the model treating species as independent observational units. The phylogenetic model (model_phylo_kidneys) serves as reference with elpd_diff = 0, while the simpler model (model_simple_kidneys) has an expected log predictive density (ELPD) that is about 10.3 units lower, with an associated standard error of 1.5. In leave-one-out cross-validation, differences exceeding approximately four times their standard error indicate strong evidence. Here, 10.3/1.5≈6.9, providing strong evidence favouring the phylogenetic model.

Brain

# Identify qualifying families (>10 unique species per family)
good_families_all <- dat_mean %>%
  filter(organ_grouped == "brain") %>%  # Brain organ only
  group_by(class, family) %>%
  summarise(n_species = n_distinct(species), .groups = "drop") %>%
  filter(n_species > 10) %>%  # species threshold
  pull(family)

# Filter main dataset - preserves all measurements for qualifying families
dat_brain_all <- dat_mean %>%
  filter(organ_grouped == "brain", 
         family %in% good_families_all)

# families per class, order and family
dat_brain_all %>% 
  distinct(class, order, family, species, .keep_all = TRUE) %>% 
  count(class, order, family, name = "n_species_unique") %>% 
  arrange(class, desc(n_species_unique))

# A tibble: 8 × 4
  class     order           family          n_species_unique
  <fct>     <fct>           <fct>                      <int>
1 Aves      Psittaciformes  Psittacidae                   39
2 Aves      Galliformes     Phasianidae                   17
3 Aves      Passeriformes   Fringillidae                  16
4 Aves      Anseriformes    Anatidae                      14
5 Mammalia  Cetartiodactyla Bovidae                       17
6 Mammalia  Primates        Cercopithecidae               11
7 Teleostei Perciformes     Cichlidae                     52
8 Teleostei Syngnathiformes Syngnathidae                  15

# Check for database/tree species mismatches
setdiff(tree$tip.label, dat_brain_all$phylo)      # Tree species absent in database

 [1] "Oreochromis_niloticus"    "Poecilia_reticulata"     
 [3] "Anguilla_anguilla"        "Pteropus_alecto"         
 [5] "Pteropus_poliocephalus"   "Pteropus_scapulatus"     
 [7] "Lasiopodomys_brandtii"    "Rattus_norvegicus"       
 [9] "Mus_musculus"             "Meriones_unguiculatus"   
[11] "Phrynocephalus_vlangalii" "Ficedula_hypoleuca"      
[13] "Padda_oryzivora"          "Lonchura_punctulata"     
[15] "Lonchura_flaviprymna"     "Lonchura_bicolor"        
[17] "Hypargos_niveoguttatus"   "Pytilia_hypogrammica"    
[19] "Uraeginthus_bengalus"     "Amandava_amandava"       
[21] "Coturnix_japonica"        "Gallus_gallus"           
[23] "Numida_meleagris"        

setdiff(dat_brain_all$phylo, tree$tip.label)      # Database species absent in tree

character(0)

# Exclude mismatched species for consistency
tree_organ <- keep.tip(tree, intersect(tree$tip.label, dat_brain_all$phylo))
dat_brain_all <- dat_brain_all[dat_brain_all$phylo %in% tree_organ$tip.label, ]

# Re-check for mismatches after pruning
setdiff(tree_organ$tip.label, dat_brain_all$phylo)

character(0)

setdiff(dat_brain_all$phylo, tree_organ$tip.label)

character(0)

# Is ultrametric?
is.ultrametric(tree_organ)

[1] TRUE

# how many species?
length(tree_organ$tip.label)

[1] 181

# Compute phylogenetic covariance matrix
A_organ <- ape::vcv.phylo(tree_organ, corr = TRUE)

Fishes - Cichlidae (cichlids)

Filter data and prune tree

# Filter full data to those families only
dat_organ_Cichlidae <- dat_brain_all %>%
         filter(family == "Cichlidae") %>%
  ungroup()

# Check for database/tree species mismatches
setdiff(tree$tip.label, dat_organ_Cichlidae$phylo)      # Tree species absent in database

  [1] "Oreochromis_niloticus"         "Poecilia_reticulata"          
  [3] "Nerophis_lumbriciformis"       "Syngnathus_abaster"           
  [5] "Syngnathus_schlegeli"          "Hippocampus_comes"            
  [7] "Hippocampus_trimaculatus"      "Hippocampus_kuda"             
  [9] "Hippocampus_spinosissimus"     "Hippocampus_abdominalis"      
 [11] "Hippichthys_cyanospilos"       "Syngnathoides_biaculeatus"    
 [13] "Corythoichthys_intestinalis"   "Corythoichthys_haematopterus" 
 [15] "Doryichthys_boaja"             "Doryrhamphus_japonicus"       
 [17] "Entelurus_aequoreus"           "Anguilla_anguilla"            
 [19] "Syncerus_caffer"               "Tragelaphus_eurycerus"        
 [21] "Tragelaphus_scriptus"          "Redunca_arundinum"            
 [23] "Antidorcas_marsupialis"        "Nanger_granti"                
 [25] "Raphicerus_campestris"         "Cephalophus_natalensis"       
 [27] "Sylvicapra_grimmia"            "Oreotragus_oreotragus"        
 [29] "Hippotragus_equinus"           "Addax_nasomaculatus"          
 [31] "Oryx_gazella"                  "Connochaetes_taurinus"        
 [33] "Damaliscus_lunatus"            "Ovis_aries"                   
 [35] "Aepyceros_melampus"            "Pteropus_alecto"              
 [37] "Pteropus_poliocephalus"        "Pteropus_scapulatus"          
 [39] "Lasiopodomys_brandtii"         "Rattus_norvegicus"            
 [41] "Mus_musculus"                  "Meriones_unguiculatus"        
 [43] "Chlorocebus_aethiops"          "Chlorocebus_sabaeus"          
 [45] "Erythrocebus_patas"            "Papio_cynocephalus"           
 [47] "Papio_anubis"                  "Cercocebus_atys"              
 [49] "Macaca_arctoides"              "Macaca_mulatta"               
 [51] "Macaca_fascicularis"           "Macaca_maura"                 
 [53] "Trachypithecus_francoisi"      "Phrynocephalus_vlangalii"     
 [55] "Platycercus_caledonicus"       "Platycercus_elegans"          
 [57] "Platycercus_eximius"           "Platycercus_venustus"         
 [59] "Barnardius_zonarius"           "Northiella_haematogaster"     
 [61] "Lathamus_discolor"             "Neophema_chrysostoma"         
 [63] "Neophema_pulchella"            "Psittacula_krameri"           
 [65] "Eclectus_roratus"              "Aprosmictus_jonquillaceus"    
 [67] "Alisterus_scapularis"          "Alisterus_amboinensis"        
 [69] "Polytelis_alexandrae"          "Trichoglossus_haematodus"     
 [71] "Agapornis_lilianae"            "Agapornis_taranta"            
 [73] "Loriculus_vernalis"            "Ara_ararauna"                 
 [75] "Guaruba_guarouba"              "Enicognathus_leptorhynchus"   
 [77] "Pionites_melanocephalus"       "Forpus_coelestis"             
 [79] "Forpus_passerinus"             "Amazona_leucocephala"         
 [81] "Amazona_albifrons"             "Amazona_pretrei"              
 [83] "Amazona_vinacea"               "Amazona_finschi"              
 [85] "Amazona_amazonica"             "Amazona_ochrocephala"         
 [87] "Amazona_aestiva"               "Brotogeris_versicolurus"      
 [89] "Brotogeris_pyrrhoptera"        "Bolborhynchus_lineola"        
 [91] "Poicephalus_gulielmi"          "Poicephalus_meyeri"           
 [93] "Psittacus_erithacus"           "Serinus_mennelli"             
 [95] "Ficedula_hypoleuca"            "Padda_oryzivora"              
 [97] "Lonchura_punctulata"           "Lonchura_flaviprymna"         
 [99] "Lonchura_bicolor"              "Hypargos_niveoguttatus"       
[101] "Pytilia_hypogrammica"          "Uraeginthus_bengalus"         
[103] "Amandava_amandava"             "Plectrophenax_nivalis"        
[105] "Serinus_canaria"               "Serinus_serinus"              
[107] "Loxia_curvirostra"             "Carduelis_carduelis"          
[109] "Carpodacus_roseus"             "Uragus_sibiricus"             
[111] "Pyrrhula_pyrrhula"             "Pinicola_enucleator"          
[113] "Bucanetes_githagineus"         "Coccothraustes_coccothraustes"
[115] "Mycerobas_affinis"             "Mycerobas_carnipes"           
[117] "Fringilla_montifringilla"      "Fringilla_coelebs"            
[119] "Anas_platyrhynchos"            "Anas_acuta"                   
[121] "Anas_crecca"                   "Mergus_serrator"              
[123] "Mergus_merganser"              "Bucephala_clangula"           
[125] "Melanitta_nigra"               "Somateria_mollissima"         
[127] "Callonetta_leucophrys"         "Branta_bernicla"              
[129] "Branta_leucopsis"              "Anser_anser"                  
[131] "Cygnus_columbianus"            "Tadorna_tadorna"              
[133] "Coturnix_japonica"             "Pucrasia_macrolopha"          
[135] "Phasianus_colchicus"           "Chrysolophus_pictus"          
[137] "Lophura_nycthemera"            "Lophura_ignita"               
[139] "Syrmaticus_ellioti"            "Syrmaticus_reevesii"          
[141] "Perdix_perdix"                 "Tetrao_urogallus"             
[143] "Lagopus_muta"                  "Lagopus_lagopus"              
[145] "Lophophorus_impejanus"         "Tragopan_temminckii"          
[147] "Pavo_cristatus"                "Gallus_gallus"                
[149] "Gallus_sonneratii"             "Rollulus_rouloul"             
[151] "Arborophila_torqueola"         "Numida_meleagris"             

setdiff(dat_organ_Cichlidae$phylo, tree$tip.label)      # Database species absent in tree

character(0)

# Exclude mismatched species for consistency
tree_organ <- keep.tip(tree, intersect(tree$tip.label, dat_organ_Cichlidae$phylo))
dat_organ_Cichlidae <- dat_organ_Cichlidae[dat_organ_Cichlidae$phylo %in% tree_organ$tip.label, ]

# Re-check for mismatches after pruning
setdiff(tree_organ$tip.label, dat_organ_Cichlidae$phylo)

character(0)

setdiff(dat_organ_Cichlidae$phylo, tree_organ$tip.label)

character(0)

# Is ultrametric?
is.ultrametric(tree_organ)

[1] TRUE

# how many species?
length(tree_organ$tip.label)

[1] 52

# Compute phylogenetic covariance matrix
A_organ <- ape::vcv.phylo(tree_organ, corr = TRUE)

Model simple

model_simple_brain_Cichlidae <- brm(
  log10_organ_size ~ 
    1 + 
    log10_body_size +
    (1 + log10_body_size | sex),
  data = dat_organ_Cichlidae,
  family = gaussian(),
    prior = c(
    prior(normal(0.75, 0.5), class = "b", coef = "log10_body_size"),
    prior(normal(0, 2), class = "Intercept"),
    prior(student_t(3, 0, 0.5), class = "sd"),
    prior(student_t(3, 0, 1),   class = "sigma")
  ),
  seed = 6955,
  sample_prior = TRUE, 
  chains = 4, 
  cores = 4, 
  threads = threading(2),
  iter = 4000, 
  warmup = 2000,
  control = list(max_treedepth = 15,
                 adapt_delta = 0.99),
  save_pars = save_pars(all = TRUE),
  silent = TRUE, refresh = 0
)

Running MCMC with 4 parallel chains, with 2 thread(s) per chain...

Chain 1 finished in 14.7 seconds.
Chain 3 finished in 17.9 seconds.
Chain 4 finished in 29.8 seconds.
Chain 2 finished in 42.6 seconds.

All 4 chains finished successfully.
Mean chain execution time: 26.3 seconds.
Total execution time: 42.8 seconds.

Model check

pp_check(model_simple_brain_Cichlidae)

Model summary

summary(model_simple_brain_Cichlidae)

 Family: gaussian 
  Links: mu = identity; sigma = identity 
Formula: log10_organ_size ~ 1 + log10_body_size + (1 + log10_body_size | sex) 
   Data: dat_organ_Cichlidae (Number of observations: 104) 
  Draws: 4 chains, each with iter = 4000; warmup = 2000; thin = 1;
         total post-warmup draws = 8000

Multilevel Hyperparameters:
~sex (Number of levels: 2) 
                               Estimate Est.Error l-95% CI u-95% CI Rhat
sd(Intercept)                      0.19      0.27     0.00     0.85 1.00
sd(log10_body_size)                0.17      0.22     0.00     0.79 1.00
cor(Intercept,log10_body_size)    -0.07      0.63    -0.98     0.96 1.00
                               Bulk_ESS Tail_ESS
sd(Intercept)                      1615     2415
sd(log10_body_size)                1567     2037
cor(Intercept,log10_body_size)     3587     4161

Regression Coefficients:
                Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept          -1.69      0.20    -2.07    -1.22 1.00     2598     2557
log10_body_size     0.58      0.16     0.29     0.97 1.00     1518     1502

Further Distributional Parameters:
      Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma     0.10      0.01     0.08     0.11 1.00     5965     5418

Draws were sampled using sample(hmc). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).

I will next extract, for each sex, the estimated slope and intercept, together with the 95% credible intervals.

# Extract combined coefficients (fixed + random)
coef(model_simple_brain_Cichlidae)$sex %>%
{tibble(
  sex = dimnames(.)[[1]],
  intercept    = .[, "Estimate", "Intercept"],
  intercept_low  = .[, "Q2.5", "Intercept"], 
  intercept_high = .[, "Q97.5", "Intercept"]
)} %>%
bind_cols(
  tibble(
    sex = dimnames(coef(model_simple_brain_Cichlidae)$sex)[[1]],
    slope = coef(model_simple_brain_Cichlidae)$sex[, "Estimate", "log10_body_size"]
  ) %>% select(slope),
  tibble(
    sex = dimnames(coef(model_simple_brain_Cichlidae)$sex)[[1]],
    slope_low  = coef(model_simple_brain_Cichlidae)$sex[, "Q2.5", "log10_body_size"],
    slope_high = coef(model_simple_brain_Cichlidae)$sex[, "Q97.5", "log10_body_size"]
  ) %>% select(slope_low, slope_high)
)

# A tibble: 2 × 7
  sex    intercept intercept_low intercept_high slope slope_low slope_high
  <chr>      <dbl>         <dbl>          <dbl> <dbl>     <dbl>      <dbl>
1 female     -1.70         -1.76          -1.64 0.561     0.508      0.612
2 male       -1.71         -1.77          -1.64 0.560     0.505      0.613

Model with phylogeny

model_phylo_brain_Cichlidae <- brm(
  log10_organ_size ~ 
    1 + 
    log10_body_size +
    (1 + log10_body_size | sex) +
    (1 | gr(phylo, cov = A_organ)),
  data = dat_organ_Cichlidae,
  data2 = list(A_organ = A_organ),
  family = gaussian(),
    prior = c(
    prior(normal(0.75, 0.5), class = "b", coef = "log10_body_size"),
    prior(normal(0, 2), class = "Intercept"),
    prior(student_t(3, 0, 0.5), class = "sd"),
    prior(student_t(3, 0, 1),   class = "sigma")
  ),
  seed = 6955,
  sample_prior = TRUE, 
  chains = 4, 
  cores = 4, 
  threads = threading(2),
  iter = 4000, 
  warmup = 2000,
  control = list(max_treedepth = 15,
                 adapt_delta = 0.99),
  save_pars = save_pars(all = TRUE),
  silent = TRUE, refresh = 0
)

Running MCMC with 4 parallel chains, with 2 thread(s) per chain...

Chain 3 finished in 78.4 seconds.
Chain 4 finished in 80.0 seconds.
Chain 2 finished in 104.5 seconds.
Chain 1 finished in 131.6 seconds.

All 4 chains finished successfully.
Mean chain execution time: 98.6 seconds.
Total execution time: 131.7 seconds.

Model check

pp_check(model_phylo_brain_Cichlidae)

Model summary

summary(model_phylo_brain_Cichlidae)

 Family: gaussian 
  Links: mu = identity; sigma = identity 
Formula: log10_organ_size ~ 1 + log10_body_size + (1 + log10_body_size | sex) + (1 | gr(phylo, cov = A_organ)) 
   Data: dat_organ_Cichlidae (Number of observations: 104) 
  Draws: 4 chains, each with iter = 4000; warmup = 2000; thin = 1;
         total post-warmup draws = 8000

Multilevel Hyperparameters:
~phylo (Number of levels: 52) 
              Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept)     0.12      0.01     0.09     0.15 1.00     1324     2282

~sex (Number of levels: 2) 
                               Estimate Est.Error l-95% CI u-95% CI Rhat
sd(Intercept)                      0.17      0.23     0.00     0.82 1.00
sd(log10_body_size)                0.13      0.20     0.00     0.67 1.00
cor(Intercept,log10_body_size)    -0.04      0.63    -0.98     0.97 1.00
                               Bulk_ESS Tail_ESS
sd(Intercept)                      2103     3504
sd(log10_body_size)                1854     3550
cor(Intercept,log10_body_size)     5275     4667

Regression Coefficients:
                Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept          -1.57      0.19    -1.95    -1.16 1.00     2008     2414
log10_body_size     0.45      0.12     0.22     0.79 1.00     1958     1836

Further Distributional Parameters:
      Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma     0.03      0.00     0.02     0.04 1.00     2126     3797

Draws were sampled using sample(hmc). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).

Phylogenetic signal

hyp <- paste(
  "sd_phylo__Intercept^2 /",
  "(sd_phylo__Intercept^2 + sd_sex__Intercept^2 + sigma^2) = 0"
)
(hyp <- hypothesis(model_phylo_brain_Cichlidae, hyp, class = NULL))

Hypothesis Tests for class :
                Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
1 (sd_phylo__Interc... = 0     0.57      0.33     0.02     0.96        0.2
  Post.Prob Star
1      0.17    *
---
'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
'*': For one-sided hypotheses, the posterior probability exceeds 95%;
for two-sided hypotheses, the value tested against lies outside the 95%-CI.
Posterior probabilities of point hypotheses assume equal prior probabilities.

lambda_brain <- hyp$hypothesis$Estimate

I will next extract, for each sex, the estimated slope and intercept, together with the 95% credible intervals.

# Extract combined coefficients (fixed + random)
coef(model_phylo_brain_Cichlidae)$sex %>%
{tibble(
  sex = dimnames(.)[[1]],
  intercept    = .[, "Estimate", "Intercept"],
  intercept_low  = .[, "Q2.5", "Intercept"], 
  intercept_high = .[, "Q97.5", "Intercept"]
)} %>%
bind_cols(
  tibble(
    sex = dimnames(coef(model_phylo_brain_Cichlidae)$sex)[[1]],
    slope = coef(model_phylo_brain_Cichlidae)$sex[, "Estimate", "log10_body_size"]
  ) %>% select(slope),
  tibble(
    sex = dimnames(coef(model_phylo_brain_Cichlidae)$sex)[[1]],
    slope_low  = coef(model_phylo_brain_Cichlidae)$sex[, "Q2.5", "log10_body_size"],
    slope_high = coef(model_phylo_brain_Cichlidae)$sex[, "Q97.5", "log10_body_size"]
  ) %>% select(slope_low, slope_high)
)

# A tibble: 2 × 7
  sex    intercept intercept_low intercept_high slope slope_low slope_high
  <chr>      <dbl>         <dbl>          <dbl> <dbl>     <dbl>      <dbl>
1 female     -1.58         -1.69          -1.47 0.430     0.383      0.479
2 male       -1.57         -1.69          -1.46 0.424     0.375      0.474

Model comparison

loo_simple <- loo(model_simple_brain_Cichlidae)
loo_phylo <- loo(model_phylo_brain_Cichlidae)
loo_compare(loo_simple, loo_phylo)

                             elpd_diff se_diff
model_phylo_brain_Cichlidae    0.0       0.0  
model_simple_brain_Cichlidae -90.6      14.5  

Fishes - Syngnathidae (seahorses, pipefishes)

Filter data and prune tree

# Filter full data to those families only
dat_organ_Syngnathidae <- dat_brain_all %>%
         filter(family == "Syngnathidae") %>%
  ungroup()

# Check for database/tree species mismatches
setdiff(tree$tip.label, dat_organ_Syngnathidae$phylo)      # Tree species absent in database

  [1] "Petrochromis_famula"             "Lobochilotes_labiatus"          
  [3] "Simochromis_diagramma"           "Petrochromis_orthognathus"      
  [5] "Ctenochromis_horei"              "Limnotilapia_dardennii"         
  [7] "Gnathochromis_pfefferi"          "Tropheus_moorii"                
  [9] "Tropheus_brichardi"              "Haplotaxodon_microlepis"        
 [11] "Perissodus_microlepis"           "Benthochromis_tricoti"          
 [13] "Cyprichromis_leptosoma"          "Greenwoodochromis_christyi"     
 [15] "Limnochromis_staneri"            "Gnathochromis_permaxillaris"    
 [17] "Baileychromis_centropomoides"    "Triglachromis_otostigma"        
 [19] "Cyphotilapia_frontosa"           "Ophthalmotilapia_ventralis"     
 [21] "Cyathopharynx_furcifer"          "Ophthalmotilapia_nasuta"        
 [23] "Ophthalmotilapia_boops"          "Aulonocranus_dewindti"          
 [25] "Ectodus_descampsii"              "Callochromis_melanostigma"      
 [27] "Xenotilapia_melanogenys"         "Xenotilapia_flavipinnis"        
 [29] "Eretmodus_cyanostictus"          "Tanganicodus_irsacae"           
 [31] "Spathodus_marlieri"              "Spathodus_erythrodon"           
 [33] "Neolamprologus_brichardi"        "Julidochromis_regani"           
 [35] "Julidochromis_marlieri"          "Neolamprologus_tetracanthus"    
 [37] "Telmatochromis_temporalis"       "Lepidiolamprologus_elongatus"   
 [39] "Lepidiolamprologus_profundicola" "Lepidiolamprologus_nkambae"     
 [41] "Altolamprologus_compressiceps"   "Neolamprologus_brevis"          
 [43] "Chalinochromis_brichardi"        "Julidochromis_ornatus"          
 [45] "Lamprologus_ornatipinnis"        "Neolamprologus_pulcher"         
 [47] "Variabilichromis_moorii"         "Neolamprologus_tretocephalus"   
 [49] "Neolamprologus_sexfasciatus"     "Trematocara_unimaculatum"       
 [51] "Hemibates_stenosoma"             "Bathybates_ferox"               
 [53] "Oreochromis_niloticus"           "Poecilia_reticulata"            
 [55] "Anguilla_anguilla"               "Syncerus_caffer"                
 [57] "Tragelaphus_eurycerus"           "Tragelaphus_scriptus"           
 [59] "Redunca_arundinum"               "Antidorcas_marsupialis"         
 [61] "Nanger_granti"                   "Raphicerus_campestris"          
 [63] "Cephalophus_natalensis"          "Sylvicapra_grimmia"             
 [65] "Oreotragus_oreotragus"           "Hippotragus_equinus"            
 [67] "Addax_nasomaculatus"             "Oryx_gazella"                   
 [69] "Connochaetes_taurinus"           "Damaliscus_lunatus"             
 [71] "Ovis_aries"                      "Aepyceros_melampus"             
 [73] "Pteropus_alecto"                 "Pteropus_poliocephalus"         
 [75] "Pteropus_scapulatus"             "Lasiopodomys_brandtii"          
 [77] "Rattus_norvegicus"               "Mus_musculus"                   
 [79] "Meriones_unguiculatus"           "Chlorocebus_aethiops"           
 [81] "Chlorocebus_sabaeus"             "Erythrocebus_patas"             
 [83] "Papio_cynocephalus"              "Papio_anubis"                   
 [85] "Cercocebus_atys"                 "Macaca_arctoides"               
 [87] "Macaca_mulatta"                  "Macaca_fascicularis"            
 [89] "Macaca_maura"                    "Trachypithecus_francoisi"       
 [91] "Phrynocephalus_vlangalii"        "Platycercus_caledonicus"        
 [93] "Platycercus_elegans"             "Platycercus_eximius"            
 [95] "Platycercus_venustus"            "Barnardius_zonarius"            
 [97] "Northiella_haematogaster"        "Lathamus_discolor"              
 [99] "Neophema_chrysostoma"            "Neophema_pulchella"             
[101] "Psittacula_krameri"              "Eclectus_roratus"               
[103] "Aprosmictus_jonquillaceus"       "Alisterus_scapularis"           
[105] "Alisterus_amboinensis"           "Polytelis_alexandrae"           
[107] "Trichoglossus_haematodus"        "Agapornis_lilianae"             
[109] "Agapornis_taranta"               "Loriculus_vernalis"             
[111] "Ara_ararauna"                    "Guaruba_guarouba"               
[113] "Enicognathus_leptorhynchus"      "Pionites_melanocephalus"        
[115] "Forpus_coelestis"                "Forpus_passerinus"              
[117] "Amazona_leucocephala"            "Amazona_albifrons"              
[119] "Amazona_pretrei"                 "Amazona_vinacea"                
[121] "Amazona_finschi"                 "Amazona_amazonica"              
[123] "Amazona_ochrocephala"            "Amazona_aestiva"                
[125] "Brotogeris_versicolurus"         "Brotogeris_pyrrhoptera"         
[127] "Bolborhynchus_lineola"           "Poicephalus_gulielmi"           
[129] "Poicephalus_meyeri"              "Psittacus_erithacus"            
[131] "Serinus_mennelli"                "Ficedula_hypoleuca"             
[133] "Padda_oryzivora"                 "Lonchura_punctulata"            
[135] "Lonchura_flaviprymna"            "Lonchura_bicolor"               
[137] "Hypargos_niveoguttatus"          "Pytilia_hypogrammica"           
[139] "Uraeginthus_bengalus"            "Amandava_amandava"              
[141] "Plectrophenax_nivalis"           "Serinus_canaria"                
[143] "Serinus_serinus"                 "Loxia_curvirostra"              
[145] "Carduelis_carduelis"             "Carpodacus_roseus"              
[147] "Uragus_sibiricus"                "Pyrrhula_pyrrhula"              
[149] "Pinicola_enucleator"             "Bucanetes_githagineus"          
[151] "Coccothraustes_coccothraustes"   "Mycerobas_affinis"              
[153] "Mycerobas_carnipes"              "Fringilla_montifringilla"       
[155] "Fringilla_coelebs"               "Anas_platyrhynchos"             
[157] "Anas_acuta"                      "Anas_crecca"                    
[159] "Mergus_serrator"                 "Mergus_merganser"               
[161] "Bucephala_clangula"              "Melanitta_nigra"                
[163] "Somateria_mollissima"            "Callonetta_leucophrys"          
[165] "Branta_bernicla"                 "Branta_leucopsis"               
[167] "Anser_anser"                     "Cygnus_columbianus"             
[169] "Tadorna_tadorna"                 "Coturnix_japonica"              
[171] "Pucrasia_macrolopha"             "Phasianus_colchicus"            
[173] "Chrysolophus_pictus"             "Lophura_nycthemera"             
[175] "Lophura_ignita"                  "Syrmaticus_ellioti"             
[177] "Syrmaticus_reevesii"             "Perdix_perdix"                  
[179] "Tetrao_urogallus"                "Lagopus_muta"                   
[181] "Lagopus_lagopus"                 "Lophophorus_impejanus"          
[183] "Tragopan_temminckii"             "Pavo_cristatus"                 
[185] "Gallus_gallus"                   "Gallus_sonneratii"              
[187] "Rollulus_rouloul"                "Arborophila_torqueola"          
[189] "Numida_meleagris"               

setdiff(dat_organ_Syngnathidae$phylo, tree$tip.label)      # Database species absent in tree

character(0)

# Exclude mismatched species for consistency
tree_organ <- keep.tip(tree, intersect(tree$tip.label, dat_organ_Syngnathidae$phylo))
dat_organ_Syngnathidae <- dat_organ_Syngnathidae[dat_organ_Syngnathidae$phylo %in% tree_organ$tip.label, ]

# Re-check for mismatches after pruning
setdiff(tree_organ$tip.label, dat_organ_Syngnathidae$phylo)

character(0)

setdiff(dat_organ_Syngnathidae$phylo, tree_organ$tip.label)

character(0)

# Is ultrametric?
is.ultrametric(tree_organ)

[1] TRUE

# how many species?
length(tree_organ$tip.label)

[1] 15

# Compute phylogenetic covariance matrix
A_organ <- ape::vcv.phylo(tree_organ, corr = TRUE)

Model simple

model_simple_brain_Syngnathidae <- brm(
  log10_organ_size ~ 
    1 + 
    log10_body_size +
    (1 + log10_body_size | sex),
  data = dat_organ_Syngnathidae,
  family = gaussian(),
    prior = c(
    prior(normal(0.75, 0.5), class = "b", coef = "log10_body_size"),
    prior(normal(0, 2), class = "Intercept"),
    prior(student_t(3, 0, 0.5), class = "sd"),
    prior(student_t(3, 0, 1),   class = "sigma")
  ),
  seed = 6955,
  sample_prior = TRUE, 
  chains = 4, 
  cores = 4, 
  threads = threading(2),
  iter = 4000, 
  warmup = 2000,
  control = list(max_treedepth = 15,
                 adapt_delta = 0.99),
  save_pars = save_pars(all = TRUE),
  silent = TRUE, refresh = 0
)

Running MCMC with 4 parallel chains, with 2 thread(s) per chain...

Chain 1 finished in 2.1 seconds.
Chain 2 finished in 2.0 seconds.
Chain 4 finished in 1.9 seconds.
Chain 3 finished in 2.1 seconds.

All 4 chains finished successfully.
Mean chain execution time: 2.0 seconds.
Total execution time: 2.2 seconds.

Model check

pp_check(model_simple_brain_Syngnathidae)

Model summary

summary(model_simple_brain_Syngnathidae)

 Family: gaussian 
  Links: mu = identity; sigma = identity 
Formula: log10_organ_size ~ 1 + log10_body_size + (1 + log10_body_size | sex) 
   Data: dat_organ_Syngnathidae (Number of observations: 30) 
  Draws: 4 chains, each with iter = 4000; warmup = 2000; thin = 1;
         total post-warmup draws = 8000

Multilevel Hyperparameters:
~sex (Number of levels: 2) 
                               Estimate Est.Error l-95% CI u-95% CI Rhat
sd(Intercept)                      0.22      0.25     0.00     0.93 1.00
sd(log10_body_size)                0.21      0.23     0.00     0.87 1.00
cor(Intercept,log10_body_size)    -0.03      0.60    -0.97     0.95 1.00
                               Bulk_ESS Tail_ESS
sd(Intercept)                      2281     2624
sd(log10_body_size)                2415     3420
cor(Intercept,log10_body_size)     4795     4767

Regression Coefficients:
                Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept          -2.36      0.21    -2.76    -1.81 1.00     2167     1947
log10_body_size     0.56      0.17     0.23     0.98 1.00     2438     2271

Further Distributional Parameters:
      Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma     0.17      0.02     0.13     0.22 1.00     6741     4508

Draws were sampled using sample(hmc). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).

I will next extract, for each sex, the estimated slope and intercept, together with the 95% credible intervals.

# Extract combined coefficients (fixed + random)
coef(model_simple_brain_Syngnathidae)$sex %>%
{tibble(
  sex = dimnames(.)[[1]],
  intercept    = .[, "Estimate", "Intercept"],
  intercept_low  = .[, "Q2.5", "Intercept"], 
  intercept_high = .[, "Q97.5", "Intercept"]
)} %>%
bind_cols(
  tibble(
    sex = dimnames(coef(model_simple_brain_Syngnathidae)$sex)[[1]],
    slope = coef(model_simple_brain_Syngnathidae)$sex[, "Estimate", "log10_body_size"]
  ) %>% select(slope),
  tibble(
    sex = dimnames(coef(model_simple_brain_Syngnathidae)$sex)[[1]],
    slope_low  = coef(model_simple_brain_Syngnathidae)$sex[, "Q2.5", "log10_body_size"],
    slope_high = coef(model_simple_brain_Syngnathidae)$sex[, "Q97.5", "log10_body_size"]
  ) %>% select(slope_low, slope_high)
)

# A tibble: 2 × 7
  sex    intercept intercept_low intercept_high slope slope_low slope_high
  <chr>      <dbl>         <dbl>          <dbl> <dbl>     <dbl>      <dbl>
1 female     -2.37         -2.46          -2.28 0.524     0.399      0.645
2 male       -2.40         -2.50          -2.31 0.535     0.411      0.667

Model with phylogeny

model_phylo_brain_Syngnathidae <- brm(
  log10_organ_size ~ 
    1 + 
    log10_body_size +
    (1 + log10_body_size | sex) +
    (1 | gr(phylo, cov = A_organ)),
  data = dat_organ_Syngnathidae,
  data2 = list(A_organ = A_organ),
  family = gaussian(),
    prior = c(
    prior(normal(0.75, 0.5), class = "b", coef = "log10_body_size"),
    prior(normal(0, 2), class = "Intercept"),
    prior(student_t(3, 0, 0.5), class = "sd"),
    prior(student_t(3, 0, 1),   class = "sigma")
  ),
  seed = 6955,
  sample_prior = TRUE, 
  chains = 4, 
  cores = 4, 
  threads = threading(2),
  iter = 4000, 
  warmup = 2000,
  control = list(max_treedepth = 15,
                 adapt_delta = 0.99),
  save_pars = save_pars(all = TRUE),
  silent = TRUE, refresh = 0
)

Running MCMC with 4 parallel chains, with 2 thread(s) per chain...

Chain 3 finished in 7.8 seconds.
Chain 4 finished in 7.9 seconds.
Chain 1 finished in 13.6 seconds.
Chain 2 finished in 14.7 seconds.

All 4 chains finished successfully.
Mean chain execution time: 11.0 seconds.
Total execution time: 14.9 seconds.

Model check

pp_check(model_phylo_brain_Syngnathidae)

Model summary

summary(model_phylo_brain_Syngnathidae)

 Family: gaussian 
  Links: mu = identity; sigma = identity 
Formula: log10_organ_size ~ 1 + log10_body_size + (1 + log10_body_size | sex) + (1 | gr(phylo, cov = A_organ)) 
   Data: dat_organ_Syngnathidae (Number of observations: 30) 
  Draws: 4 chains, each with iter = 4000; warmup = 2000; thin = 1;
         total post-warmup draws = 8000

Multilevel Hyperparameters:
~phylo (Number of levels: 15) 
              Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept)     0.22      0.06     0.13     0.35 1.00     1694     3070

~sex (Number of levels: 2) 
                               Estimate Est.Error l-95% CI u-95% CI Rhat
sd(Intercept)                      0.22      0.27     0.01     0.91 1.00
sd(log10_body_size)                0.18      0.23     0.00     0.78 1.00
cor(Intercept,log10_body_size)    -0.05      0.62    -0.98     0.96 1.00
                               Bulk_ESS Tail_ESS
sd(Intercept)                      2303     3289
sd(log10_body_size)                2967     4403
cor(Intercept,log10_body_size)     5672     4883

Regression Coefficients:
                Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept          -2.36      0.25    -2.80    -1.80 1.00     2437     1657
log10_body_size     0.55      0.17     0.25     0.98 1.00     2851     3020

Further Distributional Parameters:
      Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma     0.07      0.02     0.05     0.12 1.00     1913     3164

Draws were sampled using sample(hmc). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).

Phylogenetic signal

hyp <- paste(
  "sd_phylo__Intercept^2 /",
  "(sd_phylo__Intercept^2 + sd_sex__Intercept^2 + sigma^2) = 0"
)
(hyp <- hypothesis(model_phylo_brain_Syngnathidae, hyp, class = NULL))

Hypothesis Tests for class :
                Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
1 (sd_phylo__Interc... = 0     0.59      0.29     0.04     0.95        0.1
  Post.Prob Star
1      0.09    *
---
'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
'*': For one-sided hypotheses, the posterior probability exceeds 95%;
for two-sided hypotheses, the value tested against lies outside the 95%-CI.
Posterior probabilities of point hypotheses assume equal prior probabilities.

lambda_brain <- hyp$hypothesis$Estimate

I will next extract, for each sex, the estimated slope and intercept, together with the 95% credible intervals.

# Extract combined coefficients (fixed + random)
coef(model_phylo_brain_Syngnathidae)$sex %>%
{tibble(
  sex = dimnames(.)[[1]],
  intercept    = .[, "Estimate", "Intercept"],
  intercept_low  = .[, "Q2.5", "Intercept"], 
  intercept_high = .[, "Q97.5", "Intercept"]
)} %>%
bind_cols(
  tibble(
    sex = dimnames(coef(model_phylo_brain_Syngnathidae)$sex)[[1]],
    slope = coef(model_phylo_brain_Syngnathidae)$sex[, "Estimate", "log10_body_size"]
  ) %>% select(slope),
  tibble(
    sex = dimnames(coef(model_phylo_brain_Syngnathidae)$sex)[[1]],
    slope_low  = coef(model_phylo_brain_Syngnathidae)$sex[, "Q2.5", "log10_body_size"],
    slope_high = coef(model_phylo_brain_Syngnathidae)$sex[, "Q97.5", "log10_body_size"]
  ) %>% select(slope_low, slope_high)
)

# A tibble: 2 × 7
  sex    intercept intercept_low intercept_high slope slope_low slope_high
  <chr>      <dbl>         <dbl>          <dbl> <dbl>     <dbl>      <dbl>
1 female     -2.36         -2.57          -2.16 0.517     0.349      0.681
2 male       -2.40         -2.61          -2.20 0.535     0.358      0.706

Model comparison

loo_simple <- loo(model_simple_brain_Syngnathidae)
loo_phylo <- loo(model_phylo_brain_Syngnathidae)
loo_compare(loo_simple, loo_phylo)

                                elpd_diff se_diff
model_phylo_brain_Syngnathidae    0.0       0.0  
model_simple_brain_Syngnathidae -17.2       3.6  

Aves - Psittacidae (true parrots)

Filter data and prune tree

# Filter full data to those families only
dat_organ_Psittacidae <- dat_brain_all %>%
         filter(family == "Psittacidae") %>%
  ungroup()

# Check for database/tree species mismatches
setdiff(tree$tip.label, dat_organ_Psittacidae$phylo)      # Tree species absent in database

  [1] "Petrochromis_famula"             "Lobochilotes_labiatus"          
  [3] "Simochromis_diagramma"           "Petrochromis_orthognathus"      
  [5] "Ctenochromis_horei"              "Limnotilapia_dardennii"         
  [7] "Gnathochromis_pfefferi"          "Tropheus_moorii"                
  [9] "Tropheus_brichardi"              "Haplotaxodon_microlepis"        
 [11] "Perissodus_microlepis"           "Benthochromis_tricoti"          
 [13] "Cyprichromis_leptosoma"          "Greenwoodochromis_christyi"     
 [15] "Limnochromis_staneri"            "Gnathochromis_permaxillaris"    
 [17] "Baileychromis_centropomoides"    "Triglachromis_otostigma"        
 [19] "Cyphotilapia_frontosa"           "Ophthalmotilapia_ventralis"     
 [21] "Cyathopharynx_furcifer"          "Ophthalmotilapia_nasuta"        
 [23] "Ophthalmotilapia_boops"          "Aulonocranus_dewindti"          
 [25] "Ectodus_descampsii"              "Callochromis_melanostigma"      
 [27] "Xenotilapia_melanogenys"         "Xenotilapia_flavipinnis"        
 [29] "Eretmodus_cyanostictus"          "Tanganicodus_irsacae"           
 [31] "Spathodus_marlieri"              "Spathodus_erythrodon"           
 [33] "Neolamprologus_brichardi"        "Julidochromis_regani"           
 [35] "Julidochromis_marlieri"          "Neolamprologus_tetracanthus"    
 [37] "Telmatochromis_temporalis"       "Lepidiolamprologus_elongatus"   
 [39] "Lepidiolamprologus_profundicola" "Lepidiolamprologus_nkambae"     
 [41] "Altolamprologus_compressiceps"   "Neolamprologus_brevis"          
 [43] "Chalinochromis_brichardi"        "Julidochromis_ornatus"          
 [45] "Lamprologus_ornatipinnis"        "Neolamprologus_pulcher"         
 [47] "Variabilichromis_moorii"         "Neolamprologus_tretocephalus"   
 [49] "Neolamprologus_sexfasciatus"     "Trematocara_unimaculatum"       
 [51] "Hemibates_stenosoma"             "Bathybates_ferox"               
 [53] "Oreochromis_niloticus"           "Poecilia_reticulata"            
 [55] "Nerophis_lumbriciformis"         "Syngnathus_abaster"             
 [57] "Syngnathus_schlegeli"            "Hippocampus_comes"              
 [59] "Hippocampus_trimaculatus"        "Hippocampus_kuda"               
 [61] "Hippocampus_spinosissimus"       "Hippocampus_abdominalis"        
 [63] "Hippichthys_cyanospilos"         "Syngnathoides_biaculeatus"      
 [65] "Corythoichthys_intestinalis"     "Corythoichthys_haematopterus"   
 [67] "Doryichthys_boaja"               "Doryrhamphus_japonicus"         
 [69] "Entelurus_aequoreus"             "Anguilla_anguilla"              
 [71] "Syncerus_caffer"                 "Tragelaphus_eurycerus"          
 [73] "Tragelaphus_scriptus"            "Redunca_arundinum"              
 [75] "Antidorcas_marsupialis"          "Nanger_granti"                  
 [77] "Raphicerus_campestris"           "Cephalophus_natalensis"         
 [79] "Sylvicapra_grimmia"              "Oreotragus_oreotragus"          
 [81] "Hippotragus_equinus"             "Addax_nasomaculatus"            
 [83] "Oryx_gazella"                    "Connochaetes_taurinus"          
 [85] "Damaliscus_lunatus"              "Ovis_aries"                     
 [87] "Aepyceros_melampus"              "Pteropus_alecto"                
 [89] "Pteropus_poliocephalus"          "Pteropus_scapulatus"            
 [91] "Lasiopodomys_brandtii"           "Rattus_norvegicus"              
 [93] "Mus_musculus"                    "Meriones_unguiculatus"          
 [95] "Chlorocebus_aethiops"            "Chlorocebus_sabaeus"            
 [97] "Erythrocebus_patas"              "Papio_cynocephalus"             
 [99] "Papio_anubis"                    "Cercocebus_atys"                
[101] "Macaca_arctoides"                "Macaca_mulatta"                 
[103] "Macaca_fascicularis"             "Macaca_maura"                   
[105] "Trachypithecus_francoisi"        "Phrynocephalus_vlangalii"       
[107] "Serinus_mennelli"                "Ficedula_hypoleuca"             
[109] "Padda_oryzivora"                 "Lonchura_punctulata"            
[111] "Lonchura_flaviprymna"            "Lonchura_bicolor"               
[113] "Hypargos_niveoguttatus"          "Pytilia_hypogrammica"           
[115] "Uraeginthus_bengalus"            "Amandava_amandava"              
[117] "Plectrophenax_nivalis"           "Serinus_canaria"                
[119] "Serinus_serinus"                 "Loxia_curvirostra"              
[121] "Carduelis_carduelis"             "Carpodacus_roseus"              
[123] "Uragus_sibiricus"                "Pyrrhula_pyrrhula"              
[125] "Pinicola_enucleator"             "Bucanetes_githagineus"          
[127] "Coccothraustes_coccothraustes"   "Mycerobas_affinis"              
[129] "Mycerobas_carnipes"              "Fringilla_montifringilla"       
[131] "Fringilla_coelebs"               "Anas_platyrhynchos"             
[133] "Anas_acuta"                      "Anas_crecca"                    
[135] "Mergus_serrator"                 "Mergus_merganser"               
[137] "Bucephala_clangula"              "Melanitta_nigra"                
[139] "Somateria_mollissima"            "Callonetta_leucophrys"          
[141] "Branta_bernicla"                 "Branta_leucopsis"               
[143] "Anser_anser"                     "Cygnus_columbianus"             
[145] "Tadorna_tadorna"                 "Coturnix_japonica"              
[147] "Pucrasia_macrolopha"             "Phasianus_colchicus"            
[149] "Chrysolophus_pictus"             "Lophura_nycthemera"             
[151] "Lophura_ignita"                  "Syrmaticus_ellioti"             
[153] "Syrmaticus_reevesii"             "Perdix_perdix"                  
[155] "Tetrao_urogallus"                "Lagopus_muta"                   
[157] "Lagopus_lagopus"                 "Lophophorus_impejanus"          
[159] "Tragopan_temminckii"             "Pavo_cristatus"                 
[161] "Gallus_gallus"                   "Gallus_sonneratii"              
[163] "Rollulus_rouloul"                "Arborophila_torqueola"          
[165] "Numida_meleagris"               

setdiff(dat_organ_Psittacidae$phylo, tree$tip.label)      # Database species absent in tree

character(0)

# Exclude mismatched species for consistency
tree_organ <- keep.tip(tree, intersect(tree$tip.label, dat_organ_Psittacidae$phylo))
dat_organ_Psittacidae <- dat_organ_Psittacidae[dat_organ_Psittacidae$phylo %in% tree_organ$tip.label, ]

# Re-check for mismatches after pruning
setdiff(tree_organ$tip.label, dat_organ_Psittacidae$phylo)

character(0)

setdiff(dat_organ_Psittacidae$phylo, tree_organ$tip.label)

character(0)

# Is ultrametric?
is.ultrametric(tree_organ)

[1] TRUE

# how many species?
length(tree_organ$tip.label)

[1] 39

# Compute phylogenetic covariance matrix
A_organ <- ape::vcv.phylo(tree_organ, corr = TRUE)

Model simple

model_simple_brain_Psittacidae <- brm(
  log10_organ_size ~ 
    1 + 
    log10_body_size +
    (1 + log10_body_size | sex),
  data = dat_organ_Psittacidae,
  family = gaussian(),
    prior = c(
    prior(normal(0.75, 0.5), class = "b", coef = "log10_body_size"),
    prior(normal(0, 2), class = "Intercept"),
    prior(student_t(3, 0, 0.5), class = "sd"),
    prior(student_t(3, 0, 1),   class = "sigma")
  ),
  seed = 6955,
  sample_prior = TRUE, 
  chains = 4, 
  cores = 4, 
  threads = threading(2),
  iter = 4000, 
  warmup = 2000,
  control = list(max_treedepth = 15,
                 adapt_delta = 0.99),
  save_pars = save_pars(all = TRUE),
  silent = TRUE, refresh = 0
)

Running MCMC with 4 parallel chains, with 2 thread(s) per chain...

Chain 2 finished in 11.8 seconds.
Chain 3 finished in 12.3 seconds.
Chain 1 finished in 14.2 seconds.
Chain 4 finished in 16.0 seconds.

All 4 chains finished successfully.
Mean chain execution time: 13.6 seconds.
Total execution time: 16.2 seconds.

Model check

pp_check(model_simple_brain_Psittacidae)

Model summary

summary(model_simple_brain_Psittacidae)

 Family: gaussian 
  Links: mu = identity; sigma = identity 
Formula: log10_organ_size ~ 1 + log10_body_size + (1 + log10_body_size | sex) 
   Data: dat_organ_Psittacidae (Number of observations: 78) 
  Draws: 4 chains, each with iter = 4000; warmup = 2000; thin = 1;
         total post-warmup draws = 8000

Multilevel Hyperparameters:
~sex (Number of levels: 2) 
                               Estimate Est.Error l-95% CI u-95% CI Rhat
sd(Intercept)                      0.25      0.29     0.01     1.02 1.00
sd(log10_body_size)                0.16      0.21     0.00     0.73 1.00
cor(Intercept,log10_body_size)    -0.07      0.60    -0.97     0.95 1.00
                               Bulk_ESS Tail_ESS
sd(Intercept)                      2426     2586
sd(log10_body_size)                1635     2788
cor(Intercept,log10_body_size)     4156     4416

Regression Coefficients:
                Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept          -1.02      0.24    -1.58    -0.55 1.00     3282     3235
log10_body_size     0.75      0.13     0.44     1.02 1.00     2279     1869

Further Distributional Parameters:
      Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma     0.09      0.01     0.07     0.10 1.00     5679     4619

Draws were sampled using sample(hmc). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).

I will next extract, for each sex, the estimated slope and intercept, together with the 95% credible intervals.

# Extract combined coefficients (fixed + random)
coef(model_simple_brain_Psittacidae)$sex %>%
{tibble(
  sex = dimnames(.)[[1]],
  intercept    = .[, "Estimate", "Intercept"],
  intercept_low  = .[, "Q2.5", "Intercept"], 
  intercept_high = .[, "Q97.5", "Intercept"]
)} %>%
bind_cols(
  tibble(
    sex = dimnames(coef(model_simple_brain_Psittacidae)$sex)[[1]],
    slope = coef(model_simple_brain_Psittacidae)$sex[, "Estimate", "log10_body_size"]
  ) %>% select(slope),
  tibble(
    sex = dimnames(coef(model_simple_brain_Psittacidae)$sex)[[1]],
    slope_low  = coef(model_simple_brain_Psittacidae)$sex[, "Q2.5", "log10_body_size"],
    slope_high = coef(model_simple_brain_Psittacidae)$sex[, "Q97.5", "log10_body_size"]
  ) %>% select(slope_low, slope_high)
)

# A tibble: 2 × 7
  sex    intercept intercept_low intercept_high slope slope_low slope_high
  <chr>      <dbl>         <dbl>          <dbl> <dbl>     <dbl>      <dbl>
1 female    -1.04          -1.18         -0.914 0.765     0.705      0.832
2 male      -0.987         -1.12         -0.850 0.754     0.689      0.815

Model with phylogeny

model_phylo_brain_Psittacidae <- brm(
  log10_organ_size ~ 
    1 + 
    log10_body_size +
    (1 + log10_body_size | sex) +
    (1 | gr(phylo, cov = A_organ)),
  data = dat_organ_Psittacidae,
  data2 = list(A_organ = A_organ),
  family = gaussian(),
    prior = c(
    prior(normal(0.75, 0.5), class = "b", coef = "log10_body_size"),
    prior(normal(0, 2), class = "Intercept"),
    prior(student_t(3, 0, 0.5), class = "sd"),
    prior(student_t(3, 0, 1),   class = "sigma")
  ),
  seed = 6955,
  sample_prior = TRUE, 
  chains = 4, 
  cores = 4, 
  threads = threading(2),
  iter = 4000, 
  warmup = 2000,
  control = list(max_treedepth = 15,
                 adapt_delta = 0.99),
  save_pars = save_pars(all = TRUE),
  silent = TRUE, refresh = 0
)

Running MCMC with 4 parallel chains, with 2 thread(s) per chain...

Chain 2 finished in 36.9 seconds.
Chain 1 finished in 41.7 seconds.
Chain 3 finished in 44.2 seconds.
Chain 4 finished in 51.0 seconds.

All 4 chains finished successfully.
Mean chain execution time: 43.4 seconds.
Total execution time: 51.2 seconds.

Model check

pp_check(model_phylo_brain_Psittacidae)

Model summary

summary(model_phylo_brain_Psittacidae)

 Family: gaussian 
  Links: mu = identity; sigma = identity 
Formula: log10_organ_size ~ 1 + log10_body_size + (1 + log10_body_size | sex) + (1 | gr(phylo, cov = A_organ)) 
   Data: dat_organ_Psittacidae (Number of observations: 78) 
  Draws: 4 chains, each with iter = 4000; warmup = 2000; thin = 1;
         total post-warmup draws = 8000

Multilevel Hyperparameters:
~phylo (Number of levels: 39) 
              Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept)     0.08      0.02     0.05     0.13 1.00      975     1421

~sex (Number of levels: 2) 
                               Estimate Est.Error l-95% CI u-95% CI Rhat
sd(Intercept)                      0.26      0.29     0.01     0.99 1.00
sd(log10_body_size)                0.16      0.20     0.00     0.73 1.01
cor(Intercept,log10_body_size)    -0.09      0.60    -0.97     0.94 1.00
                               Bulk_ESS Tail_ESS
sd(Intercept)                      3149     3449
sd(log10_body_size)                2070     3355
cor(Intercept,log10_body_size)     5718     5344

Regression Coefficients:
                Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept          -0.82      0.27    -1.39    -0.27 1.00     2427     3635
log10_body_size     0.67      0.14     0.37     0.99 1.00     1825     2288

Further Distributional Parameters:
      Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma     0.05      0.01     0.04     0.07 1.00     1168     2423

Draws were sampled using sample(hmc). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).

Phylogenetic signal

hyp <- paste(
  "sd_phylo__Intercept^2 /",
  "(sd_phylo__Intercept^2 + sd_sex__Intercept^2 + sigma^2) = 0"
)
(hyp <- hypothesis(model_phylo_brain_Psittacidae, hyp, class = NULL))

Hypothesis Tests for class :
                Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
1 (sd_phylo__Interc... = 0     0.24      0.23     0.01     0.76       0.75
  Post.Prob Star
1      0.43    *
---
'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
'*': For one-sided hypotheses, the posterior probability exceeds 95%;
for two-sided hypotheses, the value tested against lies outside the 95%-CI.
Posterior probabilities of point hypotheses assume equal prior probabilities.

lambda_brain <- hyp$hypothesis$Estimate

I will next extract, for each sex, the estimated slope and intercept, together with the 95% credible intervals.

# Extract combined coefficients (fixed + random)
coef(model_phylo_brain_Psittacidae)$sex %>%
{tibble(
  sex = dimnames(.)[[1]],
  intercept    = .[, "Estimate", "Intercept"],
  intercept_low  = .[, "Q2.5", "Intercept"], 
  intercept_high = .[, "Q97.5", "Intercept"]
)} %>%
bind_cols(
  tibble(
    sex = dimnames(coef(model_phylo_brain_Psittacidae)$sex)[[1]],
    slope = coef(model_phylo_brain_Psittacidae)$sex[, "Estimate", "log10_body_size"]
  ) %>% select(slope),
  tibble(
    sex = dimnames(coef(model_phylo_brain_Psittacidae)$sex)[[1]],
    slope_low  = coef(model_phylo_brain_Psittacidae)$sex[, "Q2.5", "log10_body_size"],
    slope_high = coef(model_phylo_brain_Psittacidae)$sex[, "Q97.5", "log10_body_size"]
  ) %>% select(slope_low, slope_high)
)

# A tibble: 2 × 7
  sex    intercept intercept_low intercept_high slope slope_low slope_high
  <chr>      <dbl>         <dbl>          <dbl> <dbl>     <dbl>      <dbl>
1 female    -0.849        -1.05          -0.586 0.675     0.546      0.774
2 male      -0.778        -0.981         -0.518 0.658     0.532      0.756

Model comparison

loo_simple <- loo(model_simple_brain_Psittacidae)
loo_phylo <- loo(model_phylo_brain_Psittacidae)
loo_compare(loo_simple, loo_phylo)

                               elpd_diff se_diff
model_phylo_brain_Psittacidae    0.0       0.0  
model_simple_brain_Psittacidae -24.0       5.7  

Aves - Fringillidae (true finches)

Filter data and prune tree

# Filter full data to those families only
dat_organ_Fringillidae <- dat_brain_all %>%
         filter(family == "Fringillidae") %>%
  ungroup()

# Check for database/tree species mismatches
setdiff(tree$tip.label, dat_organ_Fringillidae$phylo)      # Tree species absent in database

  [1] "Petrochromis_famula"             "Lobochilotes_labiatus"          
  [3] "Simochromis_diagramma"           "Petrochromis_orthognathus"      
  [5] "Ctenochromis_horei"              "Limnotilapia_dardennii"         
  [7] "Gnathochromis_pfefferi"          "Tropheus_moorii"                
  [9] "Tropheus_brichardi"              "Haplotaxodon_microlepis"        
 [11] "Perissodus_microlepis"           "Benthochromis_tricoti"          
 [13] "Cyprichromis_leptosoma"          "Greenwoodochromis_christyi"     
 [15] "Limnochromis_staneri"            "Gnathochromis_permaxillaris"    
 [17] "Baileychromis_centropomoides"    "Triglachromis_otostigma"        
 [19] "Cyphotilapia_frontosa"           "Ophthalmotilapia_ventralis"     
 [21] "Cyathopharynx_furcifer"          "Ophthalmotilapia_nasuta"        
 [23] "Ophthalmotilapia_boops"          "Aulonocranus_dewindti"          
 [25] "Ectodus_descampsii"              "Callochromis_melanostigma"      
 [27] "Xenotilapia_melanogenys"         "Xenotilapia_flavipinnis"        
 [29] "Eretmodus_cyanostictus"          "Tanganicodus_irsacae"           
 [31] "Spathodus_marlieri"              "Spathodus_erythrodon"           
 [33] "Neolamprologus_brichardi"        "Julidochromis_regani"           
 [35] "Julidochromis_marlieri"          "Neolamprologus_tetracanthus"    
 [37] "Telmatochromis_temporalis"       "Lepidiolamprologus_elongatus"   
 [39] "Lepidiolamprologus_profundicola" "Lepidiolamprologus_nkambae"     
 [41] "Altolamprologus_compressiceps"   "Neolamprologus_brevis"          
 [43] "Chalinochromis_brichardi"        "Julidochromis_ornatus"          
 [45] "Lamprologus_ornatipinnis"        "Neolamprologus_pulcher"         
 [47] "Variabilichromis_moorii"         "Neolamprologus_tretocephalus"   
 [49] "Neolamprologus_sexfasciatus"     "Trematocara_unimaculatum"       
 [51] "Hemibates_stenosoma"             "Bathybates_ferox"               
 [53] "Oreochromis_niloticus"           "Poecilia_reticulata"            
 [55] "Nerophis_lumbriciformis"         "Syngnathus_abaster"             
 [57] "Syngnathus_schlegeli"            "Hippocampus_comes"              
 [59] "Hippocampus_trimaculatus"        "Hippocampus_kuda"               
 [61] "Hippocampus_spinosissimus"       "Hippocampus_abdominalis"        
 [63] "Hippichthys_cyanospilos"         "Syngnathoides_biaculeatus"      
 [65] "Corythoichthys_intestinalis"     "Corythoichthys_haematopterus"   
 [67] "Doryichthys_boaja"               "Doryrhamphus_japonicus"         
 [69] "Entelurus_aequoreus"             "Anguilla_anguilla"              
 [71] "Syncerus_caffer"                 "Tragelaphus_eurycerus"          
 [73] "Tragelaphus_scriptus"            "Redunca_arundinum"              
 [75] "Antidorcas_marsupialis"          "Nanger_granti"                  
 [77] "Raphicerus_campestris"           "Cephalophus_natalensis"         
 [79] "Sylvicapra_grimmia"              "Oreotragus_oreotragus"          
 [81] "Hippotragus_equinus"             "Addax_nasomaculatus"            
 [83] "Oryx_gazella"                    "Connochaetes_taurinus"          
 [85] "Damaliscus_lunatus"              "Ovis_aries"                     
 [87] "Aepyceros_melampus"              "Pteropus_alecto"                
 [89] "Pteropus_poliocephalus"          "Pteropus_scapulatus"            
 [91] "Lasiopodomys_brandtii"           "Rattus_norvegicus"              
 [93] "Mus_musculus"                    "Meriones_unguiculatus"          
 [95] "Chlorocebus_aethiops"            "Chlorocebus_sabaeus"            
 [97] "Erythrocebus_patas"              "Papio_cynocephalus"             
 [99] "Papio_anubis"                    "Cercocebus_atys"                
[101] "Macaca_arctoides"                "Macaca_mulatta"                 
[103] "Macaca_fascicularis"             "Macaca_maura"                   
[105] "Trachypithecus_francoisi"        "Phrynocephalus_vlangalii"       
[107] "Platycercus_caledonicus"         "Platycercus_elegans"            
[109] "Platycercus_eximius"             "Platycercus_venustus"           
[111] "Barnardius_zonarius"             "Northiella_haematogaster"       
[113] "Lathamus_discolor"               "Neophema_chrysostoma"           
[115] "Neophema_pulchella"              "Psittacula_krameri"             
[117] "Eclectus_roratus"                "Aprosmictus_jonquillaceus"      
[119] "Alisterus_scapularis"            "Alisterus_amboinensis"          
[121] "Polytelis_alexandrae"            "Trichoglossus_haematodus"       
[123] "Agapornis_lilianae"              "Agapornis_taranta"              
[125] "Loriculus_vernalis"              "Ara_ararauna"                   
[127] "Guaruba_guarouba"                "Enicognathus_leptorhynchus"     
[129] "Pionites_melanocephalus"         "Forpus_coelestis"               
[131] "Forpus_passerinus"               "Amazona_leucocephala"           
[133] "Amazona_albifrons"               "Amazona_pretrei"                
[135] "Amazona_vinacea"                 "Amazona_finschi"                
[137] "Amazona_amazonica"               "Amazona_ochrocephala"           
[139] "Amazona_aestiva"                 "Brotogeris_versicolurus"        
[141] "Brotogeris_pyrrhoptera"          "Bolborhynchus_lineola"          
[143] "Poicephalus_gulielmi"            "Poicephalus_meyeri"             
[145] "Psittacus_erithacus"             "Ficedula_hypoleuca"             
[147] "Padda_oryzivora"                 "Lonchura_punctulata"            
[149] "Lonchura_flaviprymna"            "Lonchura_bicolor"               
[151] "Hypargos_niveoguttatus"          "Pytilia_hypogrammica"           
[153] "Uraeginthus_bengalus"            "Amandava_amandava"              
[155] "Anas_platyrhynchos"              "Anas_acuta"                     
[157] "Anas_crecca"                     "Mergus_serrator"                
[159] "Mergus_merganser"                "Bucephala_clangula"             
[161] "Melanitta_nigra"                 "Somateria_mollissima"           
[163] "Callonetta_leucophrys"           "Branta_bernicla"                
[165] "Branta_leucopsis"                "Anser_anser"                    
[167] "Cygnus_columbianus"              "Tadorna_tadorna"                
[169] "Coturnix_japonica"               "Pucrasia_macrolopha"            
[171] "Phasianus_colchicus"             "Chrysolophus_pictus"            
[173] "Lophura_nycthemera"              "Lophura_ignita"                 
[175] "Syrmaticus_ellioti"              "Syrmaticus_reevesii"            
[177] "Perdix_perdix"                   "Tetrao_urogallus"               
[179] "Lagopus_muta"                    "Lagopus_lagopus"                
[181] "Lophophorus_impejanus"           "Tragopan_temminckii"            
[183] "Pavo_cristatus"                  "Gallus_gallus"                  
[185] "Gallus_sonneratii"               "Rollulus_rouloul"               
[187] "Arborophila_torqueola"           "Numida_meleagris"               

setdiff(dat_organ_Fringillidae$phylo, tree$tip.label)      # Database species absent in tree

character(0)

# Exclude mismatched species for consistency
tree_organ <- keep.tip(tree, intersect(tree$tip.label, dat_organ_Fringillidae$phylo))
dat_organ_Fringillidae <- dat_organ_Fringillidae[dat_organ_Fringillidae$phylo %in% tree_organ$tip.label, ]

# Re-check for mismatches after pruning
setdiff(tree_organ$tip.label, dat_organ_Fringillidae$phylo)

character(0)

setdiff(dat_organ_Fringillidae$phylo, tree_organ$tip.label)

character(0)

# Is ultrametric?
is.ultrametric(tree_organ)

[1] TRUE

# how many species?
length(tree_organ$tip.label)

[1] 16

# Compute phylogenetic covariance matrix
A_organ <- ape::vcv.phylo(tree_organ, corr = TRUE)

Model simple

model_simple_brain_Fringillidae <- brm(
  log10_organ_size ~ 
    1 + 
    log10_body_size +
    (1 + log10_body_size | sex),
  data = dat_organ_Fringillidae,
  family = gaussian(),
    prior = c(
    prior(normal(0.75, 0.5), class = "b", coef = "log10_body_size"),
    prior(normal(0, 2), class = "Intercept"),
    prior(student_t(3, 0, 0.5), class = "sd"),
    prior(student_t(3, 0, 1),   class = "sigma")
  ),
  sample_prior = TRUE, 
  chains = 4, 
  cores = 4, 
  threads = threading(2),
  iter = 4000, 
  warmup = 2000,
  control = list(max_treedepth = 15,
                 adapt_delta = 0.99),
  save_pars = save_pars(all = TRUE),
  silent = TRUE, refresh = 0
)

Running MCMC with 4 parallel chains, with 2 thread(s) per chain...

Chain 1 finished in 5.3 seconds.
Chain 3 finished in 6.5 seconds.
Chain 4 finished in 7.9 seconds.
Chain 2 finished in 9.1 seconds.

All 4 chains finished successfully.
Mean chain execution time: 7.2 seconds.
Total execution time: 9.3 seconds.

Model check

pp_check(model_simple_brain_Fringillidae)

Model summary

summary(model_simple_brain_Fringillidae)

 Family: gaussian 
  Links: mu = identity; sigma = identity 
Formula: log10_organ_size ~ 1 + log10_body_size + (1 + log10_body_size | sex) 
   Data: dat_organ_Fringillidae (Number of observations: 32) 
  Draws: 4 chains, each with iter = 4000; warmup = 2000; thin = 1;
         total post-warmup draws = 8000

Multilevel Hyperparameters:
~sex (Number of levels: 2) 
                               Estimate Est.Error l-95% CI u-95% CI Rhat
sd(Intercept)                      0.26      0.28     0.01     0.98 1.00
sd(log10_body_size)                0.19      0.21     0.00     0.76 1.00
cor(Intercept,log10_body_size)    -0.09      0.59    -0.97     0.94 1.00
                               Bulk_ESS Tail_ESS
sd(Intercept)                      2893     3228
sd(log10_body_size)                2216     3123
cor(Intercept,log10_body_size)     4179     4574

Regression Coefficients:
                Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept          -1.02      0.25    -1.57    -0.53 1.00     3116     3015
log10_body_size     0.71      0.16     0.37     1.05 1.00     3143     2831

Further Distributional Parameters:
      Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma     0.09      0.01     0.07     0.12 1.00     5533     4254

Draws were sampled using sample(hmc). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).

I will next extract, for each sex, the estimated slope and intercept, together with the 95% credible intervals.

# Extract combined coefficients (fixed + random)
coef(model_simple_brain_Fringillidae)$sex %>%
{tibble(
  sex = dimnames(.)[[1]],
  intercept    = .[, "Estimate", "Intercept"],
  intercept_low  = .[, "Q2.5", "Intercept"], 
  intercept_high = .[, "Q97.5", "Intercept"]
)} %>%
bind_cols(
  tibble(
    sex = dimnames(coef(model_simple_brain_Fringillidae)$sex)[[1]],
    slope = coef(model_simple_brain_Fringillidae)$sex[, "Estimate", "log10_body_size"]
  ) %>% select(slope),
  tibble(
    sex = dimnames(coef(model_simple_brain_Fringillidae)$sex)[[1]],
    slope_low  = coef(model_simple_brain_Fringillidae)$sex[, "Q2.5", "log10_body_size"],
    slope_high = coef(model_simple_brain_Fringillidae)$sex[, "Q97.5", "log10_body_size"]
  ) %>% select(slope_low, slope_high)
)

# A tibble: 2 × 7
  sex    intercept intercept_low intercept_high slope slope_low slope_high
  <chr>      <dbl>         <dbl>          <dbl> <dbl>     <dbl>      <dbl>
1 female    -0.989         -1.19         -0.779 0.693     0.541      0.840
2 male      -1.04          -1.28         -0.825 0.714     0.560      0.881

Model with phylogeny

model_phylo_brain_Fringillidae <- brm(
  log10_organ_size ~ 
    1 + 
    log10_body_size +
    (1 + log10_body_size | sex) +
    (1 | gr(phylo, cov = A_organ)),
  data = dat_organ_Fringillidae,
  data2 = list(A_organ = A_organ),
  family = gaussian(),
    prior = c(
    prior(normal(0.75, 0.5), class = "b", coef = "log10_body_size"),
    prior(normal(0, 2), class = "Intercept"),
    prior(student_t(3, 0, 0.5), class = "sd"),
    prior(student_t(3, 0, 1),   class = "sigma")
  ),
  seed = 6955,
  sample_prior = TRUE, 
  chains = 4, 
  cores = 4, 
  threads = threading(2),
  iter = 4000, 
  warmup = 2000,
  control = list(max_treedepth = 15,
                 adapt_delta = 0.99),
  save_pars = save_pars(all = TRUE),
  silent = TRUE, refresh = 0
)

Running MCMC with 4 parallel chains, with 2 thread(s) per chain...

Chain 3 finished in 11.1 seconds.
Chain 1 finished in 11.3 seconds.
Chain 4 finished in 11.3 seconds.
Chain 2 finished in 17.1 seconds.

All 4 chains finished successfully.
Mean chain execution time: 12.7 seconds.
Total execution time: 17.3 seconds.

Model check

pp_check(model_phylo_brain_Fringillidae)

Model summary

summary(model_phylo_brain_Fringillidae)

 Family: gaussian 
  Links: mu = identity; sigma = identity 
Formula: log10_organ_size ~ 1 + log10_body_size + (1 + log10_body_size | sex) + (1 | gr(phylo, cov = A_organ)) 
   Data: dat_organ_Fringillidae (Number of observations: 32) 
  Draws: 4 chains, each with iter = 4000; warmup = 2000; thin = 1;
         total post-warmup draws = 8000

Multilevel Hyperparameters:
~phylo (Number of levels: 16) 
              Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept)     0.08      0.03     0.02     0.16 1.00     1758     1740

~sex (Number of levels: 2) 
                               Estimate Est.Error l-95% CI u-95% CI Rhat
sd(Intercept)                      0.24      0.28     0.01     1.01 1.00
sd(log10_body_size)                0.18      0.21     0.00     0.76 1.00
cor(Intercept,log10_body_size)    -0.09      0.61    -0.98     0.95 1.00
                               Bulk_ESS Tail_ESS
sd(Intercept)                      2809     3504
sd(log10_body_size)                2425     4071
cor(Intercept,log10_body_size)     5171     5233

Regression Coefficients:
                Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept          -1.00      0.28    -1.55    -0.44 1.00     3009     2537
log10_body_size     0.69      0.17     0.35     1.07 1.00     2554     1871

Further Distributional Parameters:
      Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma     0.06      0.01     0.04     0.09 1.00     2083     4261

Draws were sampled using sample(hmc). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).

Phylogenetic signal

hyp <- paste(
  "sd_phylo__Intercept^2 /",
  "(sd_phylo__Intercept^2 + sd_sex__Intercept^2 + sigma^2) = 0"
)
(hyp <- hypothesis(model_phylo_brain_Fringillidae, hyp, class = NULL))

Hypothesis Tests for class :
                Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
1 (sd_phylo__Interc... = 0     0.26      0.25        0     0.81       0.76
  Post.Prob Star
1      0.43    *
---
'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
'*': For one-sided hypotheses, the posterior probability exceeds 95%;
for two-sided hypotheses, the value tested against lies outside the 95%-CI.
Posterior probabilities of point hypotheses assume equal prior probabilities.

lambda_brain <- hyp$hypothesis$Estimate

I will next extract, for each sex, the estimated slope and intercept, together with the 95% credible intervals.

# Extract combined coefficients (fixed + random)
coef(model_phylo_brain_Fringillidae)$sex %>%
{tibble(
  sex = dimnames(.)[[1]],
  intercept    = .[, "Estimate", "Intercept"],
  intercept_low  = .[, "Q2.5", "Intercept"], 
  intercept_high = .[, "Q97.5", "Intercept"]
)} %>%
bind_cols(
  tibble(
    sex = dimnames(coef(model_phylo_brain_Fringillidae)$sex)[[1]],
    slope = coef(model_phylo_brain_Fringillidae)$sex[, "Estimate", "log10_body_size"]
  ) %>% select(slope),
  tibble(
    sex = dimnames(coef(model_phylo_brain_Fringillidae)$sex)[[1]],
    slope_low  = coef(model_phylo_brain_Fringillidae)$sex[, "Q2.5", "log10_body_size"],
    slope_high = coef(model_phylo_brain_Fringillidae)$sex[, "Q97.5", "log10_body_size"]
  ) %>% select(slope_low, slope_high)
)

# A tibble: 2 × 7
  sex    intercept intercept_low intercept_high slope slope_low slope_high
  <chr>      <dbl>         <dbl>          <dbl> <dbl>     <dbl>      <dbl>
1 female    -0.982         -1.24         -0.696 0.679     0.481      0.858
2 male      -1.03          -1.31         -0.726 0.692     0.489      0.882

Model comparison

loo_simple <- loo(model_simple_brain_Fringillidae)
loo_phylo <- loo(model_phylo_brain_Fringillidae)
loo_compare(loo_simple, loo_phylo)

                                elpd_diff se_diff
model_phylo_brain_Fringillidae   0.0       0.0   
model_simple_brain_Fringillidae -3.8       2.9   

Aves - Phasianidae (chickens, turkeys, pheasants)

Filter data and prune tree

# Filter full data to those families only
dat_organ_Phasianidae <- dat_brain_all %>%
         filter(family == "Phasianidae") %>%
  ungroup()

# Check for database/tree species mismatches
setdiff(tree$tip.label, dat_organ_Phasianidae$phylo)      # Tree species absent in database

  [1] "Petrochromis_famula"             "Lobochilotes_labiatus"          
  [3] "Simochromis_diagramma"           "Petrochromis_orthognathus"      
  [5] "Ctenochromis_horei"              "Limnotilapia_dardennii"         
  [7] "Gnathochromis_pfefferi"          "Tropheus_moorii"                
  [9] "Tropheus_brichardi"              "Haplotaxodon_microlepis"        
 [11] "Perissodus_microlepis"           "Benthochromis_tricoti"          
 [13] "Cyprichromis_leptosoma"          "Greenwoodochromis_christyi"     
 [15] "Limnochromis_staneri"            "Gnathochromis_permaxillaris"    
 [17] "Baileychromis_centropomoides"    "Triglachromis_otostigma"        
 [19] "Cyphotilapia_frontosa"           "Ophthalmotilapia_ventralis"     
 [21] "Cyathopharynx_furcifer"          "Ophthalmotilapia_nasuta"        
 [23] "Ophthalmotilapia_boops"          "Aulonocranus_dewindti"          
 [25] "Ectodus_descampsii"              "Callochromis_melanostigma"      
 [27] "Xenotilapia_melanogenys"         "Xenotilapia_flavipinnis"        
 [29] "Eretmodus_cyanostictus"          "Tanganicodus_irsacae"           
 [31] "Spathodus_marlieri"              "Spathodus_erythrodon"           
 [33] "Neolamprologus_brichardi"        "Julidochromis_regani"           
 [35] "Julidochromis_marlieri"          "Neolamprologus_tetracanthus"    
 [37] "Telmatochromis_temporalis"       "Lepidiolamprologus_elongatus"   
 [39] "Lepidiolamprologus_profundicola" "Lepidiolamprologus_nkambae"     
 [41] "Altolamprologus_compressiceps"   "Neolamprologus_brevis"          
 [43] "Chalinochromis_brichardi"        "Julidochromis_ornatus"          
 [45] "Lamprologus_ornatipinnis"        "Neolamprologus_pulcher"         
 [47] "Variabilichromis_moorii"         "Neolamprologus_tretocephalus"   
 [49] "Neolamprologus_sexfasciatus"     "Trematocara_unimaculatum"       
 [51] "Hemibates_stenosoma"             "Bathybates_ferox"               
 [53] "Oreochromis_niloticus"           "Poecilia_reticulata"            
 [55] "Nerophis_lumbriciformis"         "Syngnathus_abaster"             
 [57] "Syngnathus_schlegeli"            "Hippocampus_comes"              
 [59] "Hippocampus_trimaculatus"        "Hippocampus_kuda"               
 [61] "Hippocampus_spinosissimus"       "Hippocampus_abdominalis"        
 [63] "Hippichthys_cyanospilos"         "Syngnathoides_biaculeatus"      
 [65] "Corythoichthys_intestinalis"     "Corythoichthys_haematopterus"   
 [67] "Doryichthys_boaja"               "Doryrhamphus_japonicus"         
 [69] "Entelurus_aequoreus"             "Anguilla_anguilla"              
 [71] "Syncerus_caffer"                 "Tragelaphus_eurycerus"          
 [73] "Tragelaphus_scriptus"            "Redunca_arundinum"              
 [75] "Antidorcas_marsupialis"          "Nanger_granti"                  
 [77] "Raphicerus_campestris"           "Cephalophus_natalensis"         
 [79] "Sylvicapra_grimmia"              "Oreotragus_oreotragus"          
 [81] "Hippotragus_equinus"             "Addax_nasomaculatus"            
 [83] "Oryx_gazella"                    "Connochaetes_taurinus"          
 [85] "Damaliscus_lunatus"              "Ovis_aries"                     
 [87] "Aepyceros_melampus"              "Pteropus_alecto"                
 [89] "Pteropus_poliocephalus"          "Pteropus_scapulatus"            
 [91] "Lasiopodomys_brandtii"           "Rattus_norvegicus"              
 [93] "Mus_musculus"                    "Meriones_unguiculatus"          
 [95] "Chlorocebus_aethiops"            "Chlorocebus_sabaeus"            
 [97] "Erythrocebus_patas"              "Papio_cynocephalus"             
 [99] "Papio_anubis"                    "Cercocebus_atys"                
[101] "Macaca_arctoides"                "Macaca_mulatta"                 
[103] "Macaca_fascicularis"             "Macaca_maura"                   
[105] "Trachypithecus_francoisi"        "Phrynocephalus_vlangalii"       
[107] "Platycercus_caledonicus"         "Platycercus_elegans"            
[109] "Platycercus_eximius"             "Platycercus_venustus"           
[111] "Barnardius_zonarius"             "Northiella_haematogaster"       
[113] "Lathamus_discolor"               "Neophema_chrysostoma"           
[115] "Neophema_pulchella"              "Psittacula_krameri"             
[117] "Eclectus_roratus"                "Aprosmictus_jonquillaceus"      
[119] "Alisterus_scapularis"            "Alisterus_amboinensis"          
[121] "Polytelis_alexandrae"            "Trichoglossus_haematodus"       
[123] "Agapornis_lilianae"              "Agapornis_taranta"              
[125] "Loriculus_vernalis"              "Ara_ararauna"                   
[127] "Guaruba_guarouba"                "Enicognathus_leptorhynchus"     
[129] "Pionites_melanocephalus"         "Forpus_coelestis"               
[131] "Forpus_passerinus"               "Amazona_leucocephala"           
[133] "Amazona_albifrons"               "Amazona_pretrei"                
[135] "Amazona_vinacea"                 "Amazona_finschi"                
[137] "Amazona_amazonica"               "Amazona_ochrocephala"           
[139] "Amazona_aestiva"                 "Brotogeris_versicolurus"        
[141] "Brotogeris_pyrrhoptera"          "Bolborhynchus_lineola"          
[143] "Poicephalus_gulielmi"            "Poicephalus_meyeri"             
[145] "Psittacus_erithacus"             "Serinus_mennelli"               
[147] "Ficedula_hypoleuca"              "Padda_oryzivora"                
[149] "Lonchura_punctulata"             "Lonchura_flaviprymna"           
[151] "Lonchura_bicolor"                "Hypargos_niveoguttatus"         
[153] "Pytilia_hypogrammica"            "Uraeginthus_bengalus"           
[155] "Amandava_amandava"               "Plectrophenax_nivalis"          
[157] "Serinus_canaria"                 "Serinus_serinus"                
[159] "Loxia_curvirostra"               "Carduelis_carduelis"            
[161] "Carpodacus_roseus"               "Uragus_sibiricus"               
[163] "Pyrrhula_pyrrhula"               "Pinicola_enucleator"            
[165] "Bucanetes_githagineus"           "Coccothraustes_coccothraustes"  
[167] "Mycerobas_affinis"               "Mycerobas_carnipes"             
[169] "Fringilla_montifringilla"        "Fringilla_coelebs"              
[171] "Anas_platyrhynchos"              "Anas_acuta"                     
[173] "Anas_crecca"                     "Mergus_serrator"                
[175] "Mergus_merganser"                "Bucephala_clangula"             
[177] "Melanitta_nigra"                 "Somateria_mollissima"           
[179] "Callonetta_leucophrys"           "Branta_bernicla"                
[181] "Branta_leucopsis"                "Anser_anser"                    
[183] "Cygnus_columbianus"              "Tadorna_tadorna"                
[185] "Coturnix_japonica"               "Gallus_gallus"                  
[187] "Numida_meleagris"               

setdiff(dat_organ_Phasianidae$phylo, tree$tip.label)      # Database species absent in tree

character(0)

# Exclude mismatched species for consistency
tree_organ <- keep.tip(tree, intersect(tree$tip.label, dat_organ_Phasianidae$phylo))
dat_organ_Phasianidae <- dat_organ_Phasianidae[dat_organ_Phasianidae$phylo %in% tree_organ$tip.label, ]

# Re-check for mismatches after pruning
setdiff(tree_organ$tip.label, dat_organ_Phasianidae$phylo)

character(0)

setdiff(dat_organ_Phasianidae$phylo, tree_organ$tip.label)

character(0)

# Is ultrametric?
is.ultrametric(tree_organ)

[1] TRUE

# how many species?
length(tree_organ$tip.label)

[1] 17

# Compute phylogenetic covariance matrix
A_organ <- ape::vcv.phylo(tree_organ, corr = TRUE)

Model simple

model_simple_brain_Phasianidae <- brm(
  log10_organ_size ~ 
    1 + 
    log10_body_size +
    (1 + log10_body_size | sex),
  data = dat_organ_Phasianidae,
  family = gaussian(),
    prior = c(
    prior(normal(0.75, 0.5), class = "b", coef = "log10_body_size"),
    prior(normal(0, 2), class = "Intercept"),
    prior(student_t(3, 0, 0.5), class = "sd"),
    prior(student_t(3, 0, 1),   class = "sigma")
  ),
  seed = 6955,
  sample_prior = TRUE, 
  chains = 4, 
  cores = 4, 
  threads = threading(2),
  iter = 4000, 
  warmup = 2000,
  control = list(max_treedepth = 15,
                 adapt_delta = 0.99),
  save_pars = save_pars(all = TRUE),
  silent = TRUE, refresh = 0
)

Running MCMC with 4 parallel chains, with 2 thread(s) per chain...

Chain 1 finished in 9.5 seconds.
Chain 3 finished in 11.3 seconds.
Chain 2 finished in 11.6 seconds.
Chain 4 finished in 14.2 seconds.

All 4 chains finished successfully.
Mean chain execution time: 11.6 seconds.
Total execution time: 14.3 seconds.

Model check

pp_check(model_simple_brain_Phasianidae)

Model summary

summary(model_simple_brain_Phasianidae)

 Family: gaussian 
  Links: mu = identity; sigma = identity 
Formula: log10_organ_size ~ 1 + log10_body_size + (1 + log10_body_size | sex) 
   Data: dat_organ_Phasianidae (Number of observations: 34) 
  Draws: 4 chains, each with iter = 4000; warmup = 2000; thin = 1;
         total post-warmup draws = 8000

Multilevel Hyperparameters:
~sex (Number of levels: 2) 
                               Estimate Est.Error l-95% CI u-95% CI Rhat
sd(Intercept)                      0.26      0.30     0.01     1.05 1.00
sd(log10_body_size)                0.16      0.20     0.00     0.73 1.00
cor(Intercept,log10_body_size)    -0.08      0.61    -0.98     0.95 1.00
                               Bulk_ESS Tail_ESS
sd(Intercept)                      2634     2705
sd(log10_body_size)                1380     2732
cor(Intercept,log10_body_size)     4069     3772

Regression Coefficients:
                Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept          -0.87      0.30    -1.42    -0.36 1.00     3307     3275
log10_body_size     0.49      0.14     0.24     0.82 1.00     1739     1149

Further Distributional Parameters:
      Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma     0.07      0.01     0.05     0.09 1.00     6267     5113

Draws were sampled using sample(hmc). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).

I will next extract, for each sex, the estimated slope and intercept, together with the 95% credible intervals.

# Extract combined coefficients (fixed + random)
coef(model_simple_brain_Phasianidae)$sex %>%
{tibble(
  sex = dimnames(.)[[1]],
  intercept    = .[, "Estimate", "Intercept"],
  intercept_low  = .[, "Q2.5", "Intercept"], 
  intercept_high = .[, "Q97.5", "Intercept"]
)} %>%
bind_cols(
  tibble(
    sex = dimnames(coef(model_simple_brain_Phasianidae)$sex)[[1]],
    slope = coef(model_simple_brain_Phasianidae)$sex[, "Estimate", "log10_body_size"]
  ) %>% select(slope),
  tibble(
    sex = dimnames(coef(model_simple_brain_Phasianidae)$sex)[[1]],
    slope_low  = coef(model_simple_brain_Phasianidae)$sex[, "Q2.5", "log10_body_size"],
    slope_high = coef(model_simple_brain_Phasianidae)$sex[, "Q97.5", "log10_body_size"]
  ) %>% select(slope_low, slope_high)
)

# A tibble: 2 × 7
  sex    intercept intercept_low intercept_high slope slope_low slope_high
  <chr>      <dbl>         <dbl>          <dbl> <dbl>     <dbl>      <dbl>
1 female    -0.863         -1.10         -0.628 0.480     0.396      0.563
2 male      -0.854         -1.08         -0.627 0.475     0.399      0.550

Model with phylogeny

model_phylo_brain_Phasianidae <- brm(
  log10_organ_size ~ 
    1 + 
    log10_body_size +
    (1 + log10_body_size | sex) +
    (1 | gr(phylo, cov = A_organ)),
  data = dat_organ_Phasianidae,
  data2 = list(A_organ = A_organ),
  family = gaussian(),
    prior = c(
    prior(normal(0.75, 0.5), class = "b", coef = "log10_body_size"),
    prior(normal(0, 2), class = "Intercept"),
    prior(student_t(3, 0, 0.5), class = "sd"),
    prior(student_t(3, 0, 1),   class = "sigma")
  ),
  seed = 6955,
  sample_prior = TRUE, 
  chains = 4, 
  cores = 4, 
  threads = threading(2),
  iter = 4000, 
  warmup = 2000,
  control = list(max_treedepth = 15,
                 adapt_delta = 0.99),
  save_pars = save_pars(all = TRUE),
  silent = TRUE, refresh = 0
)

Running MCMC with 4 parallel chains, with 2 thread(s) per chain...

Chain 4 finished in 22.5 seconds.
Chain 2 finished in 28.3 seconds.
Chain 1 finished in 32.4 seconds.
Chain 3 finished in 38.0 seconds.

All 4 chains finished successfully.
Mean chain execution time: 30.3 seconds.
Total execution time: 38.2 seconds.

Model check

pp_check(model_phylo_brain_Phasianidae)

Model summary

summary(model_phylo_brain_Phasianidae)

 Family: gaussian 
  Links: mu = identity; sigma = identity 
Formula: log10_organ_size ~ 1 + log10_body_size + (1 + log10_body_size | sex) + (1 | gr(phylo, cov = A_organ)) 
   Data: dat_organ_Phasianidae (Number of observations: 34) 
  Draws: 4 chains, each with iter = 4000; warmup = 2000; thin = 1;
         total post-warmup draws = 8000

Multilevel Hyperparameters:
~phylo (Number of levels: 17) 
              Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept)     0.07      0.02     0.04     0.12 1.00     1548     2328

~sex (Number of levels: 2) 
                               Estimate Est.Error l-95% CI u-95% CI Rhat
sd(Intercept)                      0.23      0.29     0.00     1.00 1.00
sd(log10_body_size)                0.13      0.18     0.00     0.62 1.00
cor(Intercept,log10_body_size)    -0.09      0.62    -0.98     0.95 1.00
                               Bulk_ESS Tail_ESS
sd(Intercept)                      2912     3607
sd(log10_body_size)                1323     3346
cor(Intercept,log10_body_size)     4308     4832

Regression Coefficients:
                Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept          -0.76      0.28    -1.35    -0.23 1.00     3345     4036
log10_body_size     0.45      0.12     0.21     0.73 1.00     2109     1973

Further Distributional Parameters:
      Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma     0.04      0.01     0.03     0.06 1.00     1979     3341

Draws were sampled using sample(hmc). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).

Phylogenetic signal

hyp <- paste(
  "sd_phylo__Intercept^2 /",
  "(sd_phylo__Intercept^2 + sd_sex__Intercept^2 + sigma^2) = 0"
)
(hyp <- hypothesis(model_phylo_brain_Phasianidae, hyp, class = NULL))

Hypothesis Tests for class :
                Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
1 (sd_phylo__Interc... = 0      0.3      0.28        0     0.86       0.68
  Post.Prob Star
1       0.4    *
---
'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
'*': For one-sided hypotheses, the posterior probability exceeds 95%;
for two-sided hypotheses, the value tested against lies outside the 95%-CI.
Posterior probabilities of point hypotheses assume equal prior probabilities.

lambda_brain <- hyp$hypothesis$Estimate

I will next extract, for each sex, the estimated slope and intercept, together with the 95% credible intervals.

# Extract combined coefficients (fixed + random)
coef(model_phylo_brain_Phasianidae)$sex %>%
{tibble(
  sex = dimnames(.)[[1]],
  intercept    = .[, "Estimate", "Intercept"],
  intercept_low  = .[, "Q2.5", "Intercept"], 
  intercept_high = .[, "Q97.5", "Intercept"]
)} %>%
bind_cols(
  tibble(
    sex = dimnames(coef(model_phylo_brain_Phasianidae)$sex)[[1]],
    slope = coef(model_phylo_brain_Phasianidae)$sex[, "Estimate", "log10_body_size"]
  ) %>% select(slope),
  tibble(
    sex = dimnames(coef(model_phylo_brain_Phasianidae)$sex)[[1]],
    slope_low  = coef(model_phylo_brain_Phasianidae)$sex[, "Q2.5", "log10_body_size"],
    slope_high = coef(model_phylo_brain_Phasianidae)$sex[, "Q97.5", "log10_body_size"]
  ) %>% select(slope_low, slope_high)
)

# A tibble: 2 × 7
  sex    intercept intercept_low intercept_high slope slope_low slope_high
  <chr>      <dbl>         <dbl>          <dbl> <dbl>     <dbl>      <dbl>
1 female    -0.756         -1.05         -0.436 0.443     0.332      0.546
2 male      -0.732         -1.01         -0.424 0.435     0.333      0.527

Model comparison

loo_simple <- loo(model_simple_brain_Phasianidae)
loo_phylo <- loo(model_phylo_brain_Phasianidae)
loo_compare(loo_simple, loo_phylo)

                               elpd_diff se_diff
model_phylo_brain_Phasianidae    0.0       0.0  
model_simple_brain_Phasianidae -11.6       3.6  

Aves - Anatidae (ducks, geese, swans)

Filter data and prune tree

# Filter full data to those families only
dat_organ_Anatidae <- dat_brain_all %>%
         filter(family == "Anatidae") %>% 
  ungroup()

# Check for database/tree species mismatches
setdiff(tree$tip.label, dat_organ_Anatidae$phylo)      # Tree species absent in database

  [1] "Petrochromis_famula"             "Lobochilotes_labiatus"          
  [3] "Simochromis_diagramma"           "Petrochromis_orthognathus"      
  [5] "Ctenochromis_horei"              "Limnotilapia_dardennii"         
  [7] "Gnathochromis_pfefferi"          "Tropheus_moorii"                
  [9] "Tropheus_brichardi"              "Haplotaxodon_microlepis"        
 [11] "Perissodus_microlepis"           "Benthochromis_tricoti"          
 [13] "Cyprichromis_leptosoma"          "Greenwoodochromis_christyi"     
 [15] "Limnochromis_staneri"            "Gnathochromis_permaxillaris"    
 [17] "Baileychromis_centropomoides"    "Triglachromis_otostigma"        
 [19] "Cyphotilapia_frontosa"           "Ophthalmotilapia_ventralis"     
 [21] "Cyathopharynx_furcifer"          "Ophthalmotilapia_nasuta"        
 [23] "Ophthalmotilapia_boops"          "Aulonocranus_dewindti"          
 [25] "Ectodus_descampsii"              "Callochromis_melanostigma"      
 [27] "Xenotilapia_melanogenys"         "Xenotilapia_flavipinnis"        
 [29] "Eretmodus_cyanostictus"          "Tanganicodus_irsacae"           
 [31] "Spathodus_marlieri"              "Spathodus_erythrodon"           
 [33] "Neolamprologus_brichardi"        "Julidochromis_regani"           
 [35] "Julidochromis_marlieri"          "Neolamprologus_tetracanthus"    
 [37] "Telmatochromis_temporalis"       "Lepidiolamprologus_elongatus"   
 [39] "Lepidiolamprologus_profundicola" "Lepidiolamprologus_nkambae"     
 [41] "Altolamprologus_compressiceps"   "Neolamprologus_brevis"          
 [43] "Chalinochromis_brichardi"        "Julidochromis_ornatus"          
 [45] "Lamprologus_ornatipinnis"        "Neolamprologus_pulcher"         
 [47] "Variabilichromis_moorii"         "Neolamprologus_tretocephalus"   
 [49] "Neolamprologus_sexfasciatus"     "Trematocara_unimaculatum"       
 [51] "Hemibates_stenosoma"             "Bathybates_ferox"               
 [53] "Oreochromis_niloticus"           "Poecilia_reticulata"            
 [55] "Nerophis_lumbriciformis"         "Syngnathus_abaster"             
 [57] "Syngnathus_schlegeli"            "Hippocampus_comes"              
 [59] "Hippocampus_trimaculatus"        "Hippocampus_kuda"               
 [61] "Hippocampus_spinosissimus"       "Hippocampus_abdominalis"        
 [63] "Hippichthys_cyanospilos"         "Syngnathoides_biaculeatus"      
 [65] "Corythoichthys_intestinalis"     "Corythoichthys_haematopterus"   
 [67] "Doryichthys_boaja"               "Doryrhamphus_japonicus"         
 [69] "Entelurus_aequoreus"             "Anguilla_anguilla"              
 [71] "Syncerus_caffer"                 "Tragelaphus_eurycerus"          
 [73] "Tragelaphus_scriptus"            "Redunca_arundinum"              
 [75] "Antidorcas_marsupialis"          "Nanger_granti"                  
 [77] "Raphicerus_campestris"           "Cephalophus_natalensis"         
 [79] "Sylvicapra_grimmia"              "Oreotragus_oreotragus"          
 [81] "Hippotragus_equinus"             "Addax_nasomaculatus"            
 [83] "Oryx_gazella"                    "Connochaetes_taurinus"          
 [85] "Damaliscus_lunatus"              "Ovis_aries"                     
 [87] "Aepyceros_melampus"              "Pteropus_alecto"                
 [89] "Pteropus_poliocephalus"          "Pteropus_scapulatus"            
 [91] "Lasiopodomys_brandtii"           "Rattus_norvegicus"              
 [93] "Mus_musculus"                    "Meriones_unguiculatus"          
 [95] "Chlorocebus_aethiops"            "Chlorocebus_sabaeus"            
 [97] "Erythrocebus_patas"              "Papio_cynocephalus"             
 [99] "Papio_anubis"                    "Cercocebus_atys"                
[101] "Macaca_arctoides"                "Macaca_mulatta"                 
[103] "Macaca_fascicularis"             "Macaca_maura"                   
[105] "Trachypithecus_francoisi"        "Phrynocephalus_vlangalii"       
[107] "Platycercus_caledonicus"         "Platycercus_elegans"            
[109] "Platycercus_eximius"             "Platycercus_venustus"           
[111] "Barnardius_zonarius"             "Northiella_haematogaster"       
[113] "Lathamus_discolor"               "Neophema_chrysostoma"           
[115] "Neophema_pulchella"              "Psittacula_krameri"             
[117] "Eclectus_roratus"                "Aprosmictus_jonquillaceus"      
[119] "Alisterus_scapularis"            "Alisterus_amboinensis"          
[121] "Polytelis_alexandrae"            "Trichoglossus_haematodus"       
[123] "Agapornis_lilianae"              "Agapornis_taranta"              
[125] "Loriculus_vernalis"              "Ara_ararauna"                   
[127] "Guaruba_guarouba"                "Enicognathus_leptorhynchus"     
[129] "Pionites_melanocephalus"         "Forpus_coelestis"               
[131] "Forpus_passerinus"               "Amazona_leucocephala"           
[133] "Amazona_albifrons"               "Amazona_pretrei"                
[135] "Amazona_vinacea"                 "Amazona_finschi"                
[137] "Amazona_amazonica"               "Amazona_ochrocephala"           
[139] "Amazona_aestiva"                 "Brotogeris_versicolurus"        
[141] "Brotogeris_pyrrhoptera"          "Bolborhynchus_lineola"          
[143] "Poicephalus_gulielmi"            "Poicephalus_meyeri"             
[145] "Psittacus_erithacus"             "Serinus_mennelli"               
[147] "Ficedula_hypoleuca"              "Padda_oryzivora"                
[149] "Lonchura_punctulata"             "Lonchura_flaviprymna"           
[151] "Lonchura_bicolor"                "Hypargos_niveoguttatus"         
[153] "Pytilia_hypogrammica"            "Uraeginthus_bengalus"           
[155] "Amandava_amandava"               "Plectrophenax_nivalis"          
[157] "Serinus_canaria"                 "Serinus_serinus"                
[159] "Loxia_curvirostra"               "Carduelis_carduelis"            
[161] "Carpodacus_roseus"               "Uragus_sibiricus"               
[163] "Pyrrhula_pyrrhula"               "Pinicola_enucleator"            
[165] "Bucanetes_githagineus"           "Coccothraustes_coccothraustes"  
[167] "Mycerobas_affinis"               "Mycerobas_carnipes"             
[169] "Fringilla_montifringilla"        "Fringilla_coelebs"              
[171] "Coturnix_japonica"               "Pucrasia_macrolopha"            
[173] "Phasianus_colchicus"             "Chrysolophus_pictus"            
[175] "Lophura_nycthemera"              "Lophura_ignita"                 
[177] "Syrmaticus_ellioti"              "Syrmaticus_reevesii"            
[179] "Perdix_perdix"                   "Tetrao_urogallus"               
[181] "Lagopus_muta"                    "Lagopus_lagopus"                
[183] "Lophophorus_impejanus"           "Tragopan_temminckii"            
[185] "Pavo_cristatus"                  "Gallus_gallus"                  
[187] "Gallus_sonneratii"               "Rollulus_rouloul"               
[189] "Arborophila_torqueola"           "Numida_meleagris"               

setdiff(dat_organ_Anatidae$phylo, tree$tip.label)      # Database species absent in tree

character(0)

# Exclude mismatched species for consistency
tree_organ <- keep.tip(tree, intersect(tree$tip.label, dat_organ_Anatidae$phylo))
dat_organ_Anatidae <- dat_organ_Anatidae[dat_organ_Anatidae$phylo %in% tree_organ$tip.label, ]

# Re-check for mismatches after pruning
setdiff(tree_organ$tip.label, dat_organ_Anatidae$phylo)

character(0)

setdiff(dat_organ_Anatidae$phylo, tree_organ$tip.label)

character(0)

# Is ultrametric?
is.ultrametric(tree_organ)

[1] TRUE

# how many species?
length(tree_organ$tip.label)

[1] 14

# Compute phylogenetic covariance matrix
A_organ <- ape::vcv.phylo(tree_organ, corr = TRUE)

Model simple

model_simple_brain_Anatidae <- brm(
  log10_organ_size ~ 
    1 + 
    log10_body_size +
    (1 + log10_body_size | sex),
  data = dat_organ_Anatidae,
  family = gaussian(),
    prior = c(
    prior(normal(0.75, 0.5), class = "b", coef = "log10_body_size"),
    prior(normal(0, 2), class = "Intercept"),
    prior(student_t(3, 0, 0.5), class = "sd"),
    prior(student_t(3, 0, 1),   class = "sigma")
  ),
  seed = 6955,
  sample_prior = TRUE, 
  chains = 4, 
  cores = 4, 
  threads = threading(2),
  iter = 4000, 
  warmup = 2000,
  control = list(max_treedepth = 15,
                 adapt_delta = 0.99),
  save_pars = save_pars(all = TRUE),
  silent = TRUE, refresh = 0
)

Running MCMC with 4 parallel chains, with 2 thread(s) per chain...

Chain 3 finished in 9.2 seconds.
Chain 2 finished in 9.8 seconds.
Chain 4 finished in 11.8 seconds.
Chain 1 finished in 26.6 seconds.

All 4 chains finished successfully.
Mean chain execution time: 14.4 seconds.
Total execution time: 26.7 seconds.

Model check

pp_check(model_simple_brain_Anatidae)

Model summary

summary(model_simple_brain_Anatidae)

 Family: gaussian 
  Links: mu = identity; sigma = identity 
Formula: log10_organ_size ~ 1 + log10_body_size + (1 + log10_body_size | sex) 
   Data: dat_organ_Anatidae (Number of observations: 28) 
  Draws: 4 chains, each with iter = 4000; warmup = 2000; thin = 1;
         total post-warmup draws = 8000

Multilevel Hyperparameters:
~sex (Number of levels: 2) 
                               Estimate Est.Error l-95% CI u-95% CI Rhat
sd(Intercept)                      0.28      0.29     0.01     1.06 1.00
sd(log10_body_size)                0.16      0.19     0.00     0.68 1.00
cor(Intercept,log10_body_size)    -0.11      0.60    -0.98     0.94 1.00
                               Bulk_ESS Tail_ESS
sd(Intercept)                      2948     3623
sd(log10_body_size)                1546     3336
cor(Intercept,log10_body_size)     4455     4715

Regression Coefficients:
                Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept          -0.85      0.28    -1.45    -0.29 1.00     3270     3706
log10_body_size     0.53      0.13     0.23     0.83 1.00     1776     1724

Further Distributional Parameters:
      Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma     0.07      0.01     0.05     0.09 1.00     5083     4416

Draws were sampled using sample(hmc). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).

I will next extract, for each sex, the estimated slope and intercept, together with the 95% credible intervals.

# Extract combined coefficients (fixed + random)
coef(model_simple_brain_Anatidae)$sex %>%
{tibble(
  sex = dimnames(.)[[1]],
  intercept    = .[, "Estimate", "Intercept"],
  intercept_low  = .[, "Q2.5", "Intercept"], 
  intercept_high = .[, "Q97.5", "Intercept"]
)} %>%
bind_cols(
  tibble(
    sex = dimnames(coef(model_simple_brain_Anatidae)$sex)[[1]],
    slope = coef(model_simple_brain_Anatidae)$sex[, "Estimate", "log10_body_size"]
  ) %>% select(slope),
  tibble(
    sex = dimnames(coef(model_simple_brain_Anatidae)$sex)[[1]],
    slope_low  = coef(model_simple_brain_Anatidae)$sex[, "Q2.5", "log10_body_size"],
    slope_high = coef(model_simple_brain_Anatidae)$sex[, "Q97.5", "log10_body_size"]
  ) %>% select(slope_low, slope_high)
)

# A tibble: 2 × 7
  sex    intercept intercept_low intercept_high slope slope_low slope_high
  <chr>      <dbl>         <dbl>          <dbl> <dbl>     <dbl>      <dbl>
1 female    -0.809         -1.05         -0.566 0.523     0.443      0.601
2 male      -0.879         -1.15         -0.623 0.536     0.455      0.624

Model with phylogeny

model_phylo_brain_Anatidae <- brm(
  log10_organ_size ~ 
    1 + 
    log10_body_size +
    (1 + log10_body_size | sex) +
    (1 | gr(phylo, cov = A_organ)),
  data = dat_organ_Anatidae,
  data2 = list(A_organ = A_organ),
  family = gaussian(),
    prior = c(
    prior(normal(0.75, 0.5), class = "b", coef = "log10_body_size"),
    prior(normal(0, 2), class = "Intercept"),
    prior(student_t(3, 0, 0.5), class = "sd"),
    prior(student_t(3, 0, 1),   class = "sigma")
  ),
  seed = 6955,
  sample_prior = TRUE, 
  chains = 4, 
  cores = 4, 
  threads = threading(2),
  iter = 4000, 
  warmup = 2000,
  control = list(max_treedepth = 15,
                 adapt_delta = 0.99),
  save_pars = save_pars(all = TRUE),
  silent = TRUE, refresh = 0
)

Running MCMC with 4 parallel chains, with 2 thread(s) per chain...

Chain 1 finished in 19.0 seconds.
Chain 4 finished in 19.6 seconds.
Chain 3 finished in 26.0 seconds.
Chain 2 finished in 56.2 seconds.

All 4 chains finished successfully.
Mean chain execution time: 30.2 seconds.
Total execution time: 56.3 seconds.

Model check

pp_check(model_phylo_brain_Anatidae)

Model summary

summary(model_phylo_brain_Anatidae)

 Family: gaussian 
  Links: mu = identity; sigma = identity 
Formula: log10_organ_size ~ 1 + log10_body_size + (1 + log10_body_size | sex) + (1 | gr(phylo, cov = A_organ)) 
   Data: dat_organ_Anatidae (Number of observations: 28) 
  Draws: 4 chains, each with iter = 4000; warmup = 2000; thin = 1;
         total post-warmup draws = 8000

Multilevel Hyperparameters:
~phylo (Number of levels: 14) 
              Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept)     0.07      0.04     0.01     0.17 1.00      911     1547

~sex (Number of levels: 2) 
                               Estimate Est.Error l-95% CI u-95% CI Rhat
sd(Intercept)                      0.28      0.32     0.01     1.08 1.00
sd(log10_body_size)                0.15      0.19     0.00     0.69 1.00
cor(Intercept,log10_body_size)    -0.10      0.60    -0.97     0.95 1.00
                               Bulk_ESS Tail_ESS
sd(Intercept)                      2623     3191
sd(log10_body_size)                2075     3836
cor(Intercept,log10_body_size)     5880     5151

Regression Coefficients:
                Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept          -0.64      0.37    -1.33     0.15 1.00     1501     1722
log10_body_size     0.47      0.14     0.18     0.77 1.00     1631     2213

Further Distributional Parameters:
      Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma     0.05      0.01     0.03     0.08 1.00     1027     1497

Draws were sampled using sample(hmc). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).

Phylogenetic signal

hyp <- paste(
  "sd_phylo__Intercept^2 /",
  "(sd_phylo__Intercept^2 + sd_sex__Intercept^2 + sigma^2) = 0"
)
(hyp <- hypothesis(model_phylo_brain_Anatidae, hyp, class = NULL))

Hypothesis Tests for class :
                Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
1 (sd_phylo__Interc... = 0     0.21      0.25        0     0.87        1.2
  Post.Prob Star
1      0.56    *
---
'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
'*': For one-sided hypotheses, the posterior probability exceeds 95%;
for two-sided hypotheses, the value tested against lies outside the 95%-CI.
Posterior probabilities of point hypotheses assume equal prior probabilities.

lambda_brain <- hyp$hypothesis$Estimate

I will next extract, for each sex, the estimated slope and intercept, together with the 95% credible intervals.

# Extract combined coefficients (fixed + random)
coef(model_phylo_brain_Anatidae)$sex %>%
{tibble(
  sex = dimnames(.)[[1]],
  intercept    = .[, "Estimate", "Intercept"],
  intercept_low  = .[, "Q2.5", "Intercept"], 
  intercept_high = .[, "Q97.5", "Intercept"]
)} %>%
bind_cols(
  tibble(
    sex = dimnames(coef(model_phylo_brain_Anatidae)$sex)[[1]],
    slope = coef(model_phylo_brain_Anatidae)$sex[, "Estimate", "log10_body_size"]
  ) %>% select(slope),
  tibble(
    sex = dimnames(coef(model_phylo_brain_Anatidae)$sex)[[1]],
    slope_low  = coef(model_phylo_brain_Anatidae)$sex[, "Q2.5", "log10_body_size"],
    slope_high = coef(model_phylo_brain_Anatidae)$sex[, "Q97.5", "log10_body_size"]
  ) %>% select(slope_low, slope_high)
)

# A tibble: 2 × 7
  sex    intercept intercept_low intercept_high slope slope_low slope_high
  <chr>      <dbl>         <dbl>          <dbl> <dbl>     <dbl>      <dbl>
1 female    -0.591        -0.985         0.0562 0.453     0.248      0.580
2 male      -0.661        -1.09          0.0292 0.467     0.253      0.604

Model comparison

loo_simple <- loo(model_simple_brain_Anatidae)
loo_phylo <- loo(model_phylo_brain_Anatidae)
loo_compare(loo_simple, loo_phylo)

                            elpd_diff se_diff
model_phylo_brain_Anatidae   0.0       0.0   
model_simple_brain_Anatidae -1.4       2.7   

Mammalia - Cercopithecidae (Old World monkeys)

Filter data and prune tree

# Filter full data to those families only
dat_organ_Cercopithecidae <- dat_brain_all %>%
         filter(family == "Cercopithecidae") %>%
  ungroup()

# Check for database/tree species mismatches
setdiff(tree$tip.label, dat_organ_Cercopithecidae$phylo)      # Tree species absent in database

  [1] "Petrochromis_famula"             "Lobochilotes_labiatus"          
  [3] "Simochromis_diagramma"           "Petrochromis_orthognathus"      
  [5] "Ctenochromis_horei"              "Limnotilapia_dardennii"         
  [7] "Gnathochromis_pfefferi"          "Tropheus_moorii"                
  [9] "Tropheus_brichardi"              "Haplotaxodon_microlepis"        
 [11] "Perissodus_microlepis"           "Benthochromis_tricoti"          
 [13] "Cyprichromis_leptosoma"          "Greenwoodochromis_christyi"     
 [15] "Limnochromis_staneri"            "Gnathochromis_permaxillaris"    
 [17] "Baileychromis_centropomoides"    "Triglachromis_otostigma"        
 [19] "Cyphotilapia_frontosa"           "Ophthalmotilapia_ventralis"     
 [21] "Cyathopharynx_furcifer"          "Ophthalmotilapia_nasuta"        
 [23] "Ophthalmotilapia_boops"          "Aulonocranus_dewindti"          
 [25] "Ectodus_descampsii"              "Callochromis_melanostigma"      
 [27] "Xenotilapia_melanogenys"         "Xenotilapia_flavipinnis"        
 [29] "Eretmodus_cyanostictus"          "Tanganicodus_irsacae"           
 [31] "Spathodus_marlieri"              "Spathodus_erythrodon"           
 [33] "Neolamprologus_brichardi"        "Julidochromis_regani"           
 [35] "Julidochromis_marlieri"          "Neolamprologus_tetracanthus"    
 [37] "Telmatochromis_temporalis"       "Lepidiolamprologus_elongatus"   
 [39] "Lepidiolamprologus_profundicola" "Lepidiolamprologus_nkambae"     
 [41] "Altolamprologus_compressiceps"   "Neolamprologus_brevis"          
 [43] "Chalinochromis_brichardi"        "Julidochromis_ornatus"          
 [45] "Lamprologus_ornatipinnis"        "Neolamprologus_pulcher"         
 [47] "Variabilichromis_moorii"         "Neolamprologus_tretocephalus"   
 [49] "Neolamprologus_sexfasciatus"     "Trematocara_unimaculatum"       
 [51] "Hemibates_stenosoma"             "Bathybates_ferox"               
 [53] "Oreochromis_niloticus"           "Poecilia_reticulata"            
 [55] "Nerophis_lumbriciformis"         "Syngnathus_abaster"             
 [57] "Syngnathus_schlegeli"            "Hippocampus_comes"              
 [59] "Hippocampus_trimaculatus"        "Hippocampus_kuda"               
 [61] "Hippocampus_spinosissimus"       "Hippocampus_abdominalis"        
 [63] "Hippichthys_cyanospilos"         "Syngnathoides_biaculeatus"      
 [65] "Corythoichthys_intestinalis"     "Corythoichthys_haematopterus"   
 [67] "Doryichthys_boaja"               "Doryrhamphus_japonicus"         
 [69] "Entelurus_aequoreus"             "Anguilla_anguilla"              
 [71] "Syncerus_caffer"                 "Tragelaphus_eurycerus"          
 [73] "Tragelaphus_scriptus"            "Redunca_arundinum"              
 [75] "Antidorcas_marsupialis"          "Nanger_granti"                  
 [77] "Raphicerus_campestris"           "Cephalophus_natalensis"         
 [79] "Sylvicapra_grimmia"              "Oreotragus_oreotragus"          
 [81] "Hippotragus_equinus"             "Addax_nasomaculatus"            
 [83] "Oryx_gazella"                    "Connochaetes_taurinus"          
 [85] "Damaliscus_lunatus"              "Ovis_aries"                     
 [87] "Aepyceros_melampus"              "Pteropus_alecto"                
 [89] "Pteropus_poliocephalus"          "Pteropus_scapulatus"            
 [91] "Lasiopodomys_brandtii"           "Rattus_norvegicus"              
 [93] "Mus_musculus"                    "Meriones_unguiculatus"          
 [95] "Phrynocephalus_vlangalii"        "Platycercus_caledonicus"        
 [97] "Platycercus_elegans"             "Platycercus_eximius"            
 [99] "Platycercus_venustus"            "Barnardius_zonarius"            
[101] "Northiella_haematogaster"        "Lathamus_discolor"              
[103] "Neophema_chrysostoma"            "Neophema_pulchella"             
[105] "Psittacula_krameri"              "Eclectus_roratus"               
[107] "Aprosmictus_jonquillaceus"       "Alisterus_scapularis"           
[109] "Alisterus_amboinensis"           "Polytelis_alexandrae"           
[111] "Trichoglossus_haematodus"        "Agapornis_lilianae"             
[113] "Agapornis_taranta"               "Loriculus_vernalis"             
[115] "Ara_ararauna"                    "Guaruba_guarouba"               
[117] "Enicognathus_leptorhynchus"      "Pionites_melanocephalus"        
[119] "Forpus_coelestis"                "Forpus_passerinus"              
[121] "Amazona_leucocephala"            "Amazona_albifrons"              
[123] "Amazona_pretrei"                 "Amazona_vinacea"                
[125] "Amazona_finschi"                 "Amazona_amazonica"              
[127] "Amazona_ochrocephala"            "Amazona_aestiva"                
[129] "Brotogeris_versicolurus"         "Brotogeris_pyrrhoptera"         
[131] "Bolborhynchus_lineola"           "Poicephalus_gulielmi"           
[133] "Poicephalus_meyeri"              "Psittacus_erithacus"            
[135] "Serinus_mennelli"                "Ficedula_hypoleuca"             
[137] "Padda_oryzivora"                 "Lonchura_punctulata"            
[139] "Lonchura_flaviprymna"            "Lonchura_bicolor"               
[141] "Hypargos_niveoguttatus"          "Pytilia_hypogrammica"           
[143] "Uraeginthus_bengalus"            "Amandava_amandava"              
[145] "Plectrophenax_nivalis"           "Serinus_canaria"                
[147] "Serinus_serinus"                 "Loxia_curvirostra"              
[149] "Carduelis_carduelis"             "Carpodacus_roseus"              
[151] "Uragus_sibiricus"                "Pyrrhula_pyrrhula"              
[153] "Pinicola_enucleator"             "Bucanetes_githagineus"          
[155] "Coccothraustes_coccothraustes"   "Mycerobas_affinis"              
[157] "Mycerobas_carnipes"              "Fringilla_montifringilla"       
[159] "Fringilla_coelebs"               "Anas_platyrhynchos"             
[161] "Anas_acuta"                      "Anas_crecca"                    
[163] "Mergus_serrator"                 "Mergus_merganser"               
[165] "Bucephala_clangula"              "Melanitta_nigra"                
[167] "Somateria_mollissima"            "Callonetta_leucophrys"          
[169] "Branta_bernicla"                 "Branta_leucopsis"               
[171] "Anser_anser"                     "Cygnus_columbianus"             
[173] "Tadorna_tadorna"                 "Coturnix_japonica"              
[175] "Pucrasia_macrolopha"             "Phasianus_colchicus"            
[177] "Chrysolophus_pictus"             "Lophura_nycthemera"             
[179] "Lophura_ignita"                  "Syrmaticus_ellioti"             
[181] "Syrmaticus_reevesii"             "Perdix_perdix"                  
[183] "Tetrao_urogallus"                "Lagopus_muta"                   
[185] "Lagopus_lagopus"                 "Lophophorus_impejanus"          
[187] "Tragopan_temminckii"             "Pavo_cristatus"                 
[189] "Gallus_gallus"                   "Gallus_sonneratii"              
[191] "Rollulus_rouloul"                "Arborophila_torqueola"          
[193] "Numida_meleagris"               

setdiff(dat_organ_Cercopithecidae$phylo, tree$tip.label)      # Database species absent in tree

character(0)

# Exclude mismatched species for consistency
tree_organ <- keep.tip(tree, intersect(tree$tip.label, dat_organ_Cercopithecidae$phylo))
dat_organ_Cercopithecidae <- dat_organ_Cercopithecidae[dat_organ_Cercopithecidae$phylo %in% tree_organ$tip.label, ]

# Re-check for mismatches after pruning
setdiff(tree_organ$tip.label, dat_organ_Cercopithecidae$phylo)

character(0)

setdiff(dat_organ_Cercopithecidae$phylo, tree_organ$tip.label)

character(0)

# Is ultrametric?
is.ultrametric(tree_organ)

[1] TRUE

# how many species?
length(tree_organ$tip.label)

[1] 11

# Compute phylogenetic covariance matrix
A_organ <- ape::vcv.phylo(tree_organ, corr = TRUE)

Model simple

model_simple_brain_Cercopithecidae <- brm(
  log10_organ_size ~ 
    1 + 
    log10_body_size +
    (1 + log10_body_size | sex),
  data = dat_organ_Cercopithecidae,
  family = gaussian(),
    prior = c(
    prior(normal(0.75, 0.5), class = "b", coef = "log10_body_size"),
    prior(normal(0, 2), class = "Intercept"),
    prior(student_t(3, 0, 0.5), class = "sd"),
    prior(student_t(3, 0, 1),   class = "sigma")
  ),
  seed = 6955,
  sample_prior = TRUE, 
  chains = 4, 
  cores = 4, 
  threads = threading(2),
  iter = 4000, 
  warmup = 2000,
  control = list(max_treedepth = 15,
                 adapt_delta = 0.99),
  save_pars = save_pars(all = TRUE),
  silent = TRUE, refresh = 0
)

Running MCMC with 4 parallel chains, with 2 thread(s) per chain...

Chain 4 finished in 5.8 seconds.
Chain 2 finished in 6.5 seconds.
Chain 3 finished in 6.6 seconds.
Chain 1 finished in 7.1 seconds.

All 4 chains finished successfully.
Mean chain execution time: 6.5 seconds.
Total execution time: 7.2 seconds.

Model check

pp_check(model_simple_brain_Cercopithecidae)

Model summary

summary(model_simple_brain_Cercopithecidae)

 Family: gaussian 
  Links: mu = identity; sigma = identity 
Formula: log10_organ_size ~ 1 + log10_body_size + (1 + log10_body_size | sex) 
   Data: dat_organ_Cercopithecidae (Number of observations: 22) 
  Draws: 4 chains, each with iter = 4000; warmup = 2000; thin = 1;
         total post-warmup draws = 8000

Multilevel Hyperparameters:
~sex (Number of levels: 2) 
                               Estimate Est.Error l-95% CI u-95% CI Rhat
sd(Intercept)                      0.34      0.36     0.01     1.27 1.00
sd(log10_body_size)                0.17      0.19     0.00     0.70 1.00
cor(Intercept,log10_body_size)    -0.13      0.59    -0.98     0.94 1.00
                               Bulk_ESS Tail_ESS
sd(Intercept)                      2810     3337
sd(log10_body_size)                1672     2989
cor(Intercept,log10_body_size)     3602     4349

Regression Coefficients:
                Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept           0.14      0.60    -1.11     1.30 1.00     5934     4770
log10_body_size     0.48      0.18     0.10     0.84 1.00     3474     3151

Further Distributional Parameters:
      Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma     0.12      0.02     0.09     0.18 1.00     5974     4533

Draws were sampled using sample(hmc). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).

I will next extract, for each sex, the estimated slope and intercept, together with the 95% credible intervals.

# Extract combined coefficients (fixed + random)
coef(model_simple_brain_Cercopithecidae)$sex %>%
{tibble(
  sex = dimnames(.)[[1]],
  intercept    = .[, "Estimate", "Intercept"],
  intercept_low  = .[, "Q2.5", "Intercept"], 
  intercept_high = .[, "Q97.5", "Intercept"]
)} %>%
bind_cols(
  tibble(
    sex = dimnames(coef(model_simple_brain_Cercopithecidae)$sex)[[1]],
    slope = coef(model_simple_brain_Cercopithecidae)$sex[, "Estimate", "log10_body_size"]
  ) %>% select(slope),
  tibble(
    sex = dimnames(coef(model_simple_brain_Cercopithecidae)$sex)[[1]],
    slope_low  = coef(model_simple_brain_Cercopithecidae)$sex[, "Q2.5", "log10_body_size"],
    slope_high = coef(model_simple_brain_Cercopithecidae)$sex[, "Q97.5", "log10_body_size"]
  ) %>% select(slope_low, slope_high)
)

# A tibble: 2 × 7
  sex    intercept intercept_low intercept_high slope slope_low slope_high
  <chr>      <dbl>         <dbl>          <dbl> <dbl>     <dbl>      <dbl>
1 female     0.173        -0.910           1.20 0.486     0.210      0.780
2 male       0.168        -0.900           1.19 0.482     0.213      0.763

Model with phylogeny

model_phylo_brain_Cercopithecidae <- brm(
  log10_organ_size ~ 
    1 + 
    log10_body_size +
    (1 + log10_body_size | sex) +
    (1 | gr(phylo, cov = A_organ)),
  data = dat_organ_Cercopithecidae,
  data2 = list(A_organ = A_organ),
  family = gaussian(),
    prior = c(
    prior(normal(0.75, 0.5), class = "b", coef = "log10_body_size"),
    prior(normal(0, 2), class = "Intercept"),
    prior(student_t(3, 0, 0.5), class = "sd"),
    prior(student_t(3, 0, 1),   class = "sigma")
  ),
  seed = 6955,
  sample_prior = TRUE, 
  chains = 4, 
  cores = 4, 
  threads = threading(2),
  iter = 4000, 
  warmup = 2000,
  control = list(max_treedepth = 15,
                 adapt_delta = 0.99),
  save_pars = save_pars(all = TRUE),
  silent = TRUE, refresh = 0
)

Running MCMC with 4 parallel chains, with 2 thread(s) per chain...

Chain 4 finished in 47.3 seconds.
Chain 2 finished in 53.6 seconds.
Chain 3 finished in 53.9 seconds.
Chain 1 finished in 59.3 seconds.

All 4 chains finished successfully.
Mean chain execution time: 53.5 seconds.
Total execution time: 59.4 seconds.

Model check

pp_check(model_phylo_brain_Cercopithecidae)

Model summary

summary(model_phylo_brain_Cercopithecidae)

 Family: gaussian 
  Links: mu = identity; sigma = identity 
Formula: log10_organ_size ~ 1 + log10_body_size + (1 + log10_body_size | sex) + (1 | gr(phylo, cov = A_organ)) 
   Data: dat_organ_Cercopithecidae (Number of observations: 22) 
  Draws: 4 chains, each with iter = 4000; warmup = 2000; thin = 1;
         total post-warmup draws = 8000

Multilevel Hyperparameters:
~phylo (Number of levels: 11) 
              Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept)     0.18      0.05     0.11     0.30 1.00     1656     2863

~sex (Number of levels: 2) 
                               Estimate Est.Error l-95% CI u-95% CI Rhat
sd(Intercept)                      0.28      0.32     0.01     1.14 1.00
sd(log10_body_size)                0.15      0.19     0.00     0.66 1.00
cor(Intercept,log10_body_size)    -0.09      0.60    -0.98     0.95 1.00
                               Bulk_ESS Tail_ESS
sd(Intercept)                      3340     3599
sd(log10_body_size)                1927     4060
cor(Intercept,log10_body_size)     4626     4229

Regression Coefficients:
                Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept           1.66      0.47     0.60     2.48 1.00     2504     2735
log10_body_size     0.09      0.15    -0.20     0.42 1.00     2241     2843

Further Distributional Parameters:
      Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma     0.02      0.01     0.01     0.04 1.00     1766     2472

Draws were sampled using sample(hmc). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).

Phylogenetic signal

hyp <- paste(
  "sd_phylo__Intercept^2 /",
  "(sd_phylo__Intercept^2 + sd_sex__Intercept^2 + sigma^2) = 0"
)
(hyp <- hypothesis(model_phylo_brain_Cercopithecidae, hyp, class = NULL))

Hypothesis Tests for class :
                Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
1 (sd_phylo__Interc... = 0     0.49      0.33     0.02     0.99       0.23
  Post.Prob Star
1      0.18    *
---
'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
'*': For one-sided hypotheses, the posterior probability exceeds 95%;
for two-sided hypotheses, the value tested against lies outside the 95%-CI.
Posterior probabilities of point hypotheses assume equal prior probabilities.

lambda_brain <- hyp$hypothesis$Estimate

I will next extract, for each sex, the estimated slope and intercept, together with the 95% credible intervals.

# Extract combined coefficients (fixed + random)
coef(model_phylo_brain_Cercopithecidae)$sex %>%
{tibble(
  sex = dimnames(.)[[1]],
  intercept    = .[, "Estimate", "Intercept"],
  intercept_low  = .[, "Q2.5", "Intercept"], 
  intercept_high = .[, "Q97.5", "Intercept"]
)} %>%
bind_cols(
  tibble(
    sex = dimnames(coef(model_phylo_brain_Cercopithecidae)$sex)[[1]],
    slope = coef(model_phylo_brain_Cercopithecidae)$sex[, "Estimate", "log10_body_size"]
  ) %>% select(slope),
  tibble(
    sex = dimnames(coef(model_phylo_brain_Cercopithecidae)$sex)[[1]],
    slope_low  = coef(model_phylo_brain_Cercopithecidae)$sex[, "Q2.5", "log10_body_size"],
    slope_high = coef(model_phylo_brain_Cercopithecidae)$sex[, "Q97.5", "log10_body_size"]
  ) %>% select(slope_low, slope_high)
)

# A tibble: 2 × 7
  sex    intercept intercept_low intercept_high  slope slope_low slope_high
  <chr>      <dbl>         <dbl>          <dbl>  <dbl>     <dbl>      <dbl>
1 female      1.72         0.872           2.41 0.0658   -0.109       0.289
2 male        1.68         0.858           2.35 0.0833   -0.0776      0.296

Model comparison

loo_simple <- loo(model_simple_brain_Cercopithecidae)
loo_phylo <- loo(model_phylo_brain_Cercopithecidae)
loo_compare(loo_simple, loo_phylo)

                                   elpd_diff se_diff
model_phylo_brain_Cercopithecidae    0.0       0.0  
model_simple_brain_Cercopithecidae -31.7       3.0  

Mammalia - Bovidae (cattle, bison, buffalo, antelopes)

Filter data and prune tree

# Filter full data to those families only
dat_organ_Bovidae <- dat_brain_all %>%
         filter(family == "Bovidae") %>%
  ungroup()

# Check for database/tree species mismatches
setdiff(tree$tip.label, dat_organ_Bovidae$phylo)      # Tree species absent in database

  [1] "Petrochromis_famula"             "Lobochilotes_labiatus"          
  [3] "Simochromis_diagramma"           "Petrochromis_orthognathus"      
  [5] "Ctenochromis_horei"              "Limnotilapia_dardennii"         
  [7] "Gnathochromis_pfefferi"          "Tropheus_moorii"                
  [9] "Tropheus_brichardi"              "Haplotaxodon_microlepis"        
 [11] "Perissodus_microlepis"           "Benthochromis_tricoti"          
 [13] "Cyprichromis_leptosoma"          "Greenwoodochromis_christyi"     
 [15] "Limnochromis_staneri"            "Gnathochromis_permaxillaris"    
 [17] "Baileychromis_centropomoides"    "Triglachromis_otostigma"        
 [19] "Cyphotilapia_frontosa"           "Ophthalmotilapia_ventralis"     
 [21] "Cyathopharynx_furcifer"          "Ophthalmotilapia_nasuta"        
 [23] "Ophthalmotilapia_boops"          "Aulonocranus_dewindti"          
 [25] "Ectodus_descampsii"              "Callochromis_melanostigma"      
 [27] "Xenotilapia_melanogenys"         "Xenotilapia_flavipinnis"        
 [29] "Eretmodus_cyanostictus"          "Tanganicodus_irsacae"           
 [31] "Spathodus_marlieri"              "Spathodus_erythrodon"           
 [33] "Neolamprologus_brichardi"        "Julidochromis_regani"           
 [35] "Julidochromis_marlieri"          "Neolamprologus_tetracanthus"    
 [37] "Telmatochromis_temporalis"       "Lepidiolamprologus_elongatus"   
 [39] "Lepidiolamprologus_profundicola" "Lepidiolamprologus_nkambae"     
 [41] "Altolamprologus_compressiceps"   "Neolamprologus_brevis"          
 [43] "Chalinochromis_brichardi"        "Julidochromis_ornatus"          
 [45] "Lamprologus_ornatipinnis"        "Neolamprologus_pulcher"         
 [47] "Variabilichromis_moorii"         "Neolamprologus_tretocephalus"   
 [49] "Neolamprologus_sexfasciatus"     "Trematocara_unimaculatum"       
 [51] "Hemibates_stenosoma"             "Bathybates_ferox"               
 [53] "Oreochromis_niloticus"           "Poecilia_reticulata"            
 [55] "Nerophis_lumbriciformis"         "Syngnathus_abaster"             
 [57] "Syngnathus_schlegeli"            "Hippocampus_comes"              
 [59] "Hippocampus_trimaculatus"        "Hippocampus_kuda"               
 [61] "Hippocampus_spinosissimus"       "Hippocampus_abdominalis"        
 [63] "Hippichthys_cyanospilos"         "Syngnathoides_biaculeatus"      
 [65] "Corythoichthys_intestinalis"     "Corythoichthys_haematopterus"   
 [67] "Doryichthys_boaja"               "Doryrhamphus_japonicus"         
 [69] "Entelurus_aequoreus"             "Anguilla_anguilla"              
 [71] "Pteropus_alecto"                 "Pteropus_poliocephalus"         
 [73] "Pteropus_scapulatus"             "Lasiopodomys_brandtii"          
 [75] "Rattus_norvegicus"               "Mus_musculus"                   
 [77] "Meriones_unguiculatus"           "Chlorocebus_aethiops"           
 [79] "Chlorocebus_sabaeus"             "Erythrocebus_patas"             
 [81] "Papio_cynocephalus"              "Papio_anubis"                   
 [83] "Cercocebus_atys"                 "Macaca_arctoides"               
 [85] "Macaca_mulatta"                  "Macaca_fascicularis"            
 [87] "Macaca_maura"                    "Trachypithecus_francoisi"       
 [89] "Phrynocephalus_vlangalii"        "Platycercus_caledonicus"        
 [91] "Platycercus_elegans"             "Platycercus_eximius"            
 [93] "Platycercus_venustus"            "Barnardius_zonarius"            
 [95] "Northiella_haematogaster"        "Lathamus_discolor"              
 [97] "Neophema_chrysostoma"            "Neophema_pulchella"             
 [99] "Psittacula_krameri"              "Eclectus_roratus"               
[101] "Aprosmictus_jonquillaceus"       "Alisterus_scapularis"           
[103] "Alisterus_amboinensis"           "Polytelis_alexandrae"           
[105] "Trichoglossus_haematodus"        "Agapornis_lilianae"             
[107] "Agapornis_taranta"               "Loriculus_vernalis"             
[109] "Ara_ararauna"                    "Guaruba_guarouba"               
[111] "Enicognathus_leptorhynchus"      "Pionites_melanocephalus"        
[113] "Forpus_coelestis"                "Forpus_passerinus"              
[115] "Amazona_leucocephala"            "Amazona_albifrons"              
[117] "Amazona_pretrei"                 "Amazona_vinacea"                
[119] "Amazona_finschi"                 "Amazona_amazonica"              
[121] "Amazona_ochrocephala"            "Amazona_aestiva"                
[123] "Brotogeris_versicolurus"         "Brotogeris_pyrrhoptera"         
[125] "Bolborhynchus_lineola"           "Poicephalus_gulielmi"           
[127] "Poicephalus_meyeri"              "Psittacus_erithacus"            
[129] "Serinus_mennelli"                "Ficedula_hypoleuca"             
[131] "Padda_oryzivora"                 "Lonchura_punctulata"            
[133] "Lonchura_flaviprymna"            "Lonchura_bicolor"               
[135] "Hypargos_niveoguttatus"          "Pytilia_hypogrammica"           
[137] "Uraeginthus_bengalus"            "Amandava_amandava"              
[139] "Plectrophenax_nivalis"           "Serinus_canaria"                
[141] "Serinus_serinus"                 "Loxia_curvirostra"              
[143] "Carduelis_carduelis"             "Carpodacus_roseus"              
[145] "Uragus_sibiricus"                "Pyrrhula_pyrrhula"              
[147] "Pinicola_enucleator"             "Bucanetes_githagineus"          
[149] "Coccothraustes_coccothraustes"   "Mycerobas_affinis"              
[151] "Mycerobas_carnipes"              "Fringilla_montifringilla"       
[153] "Fringilla_coelebs"               "Anas_platyrhynchos"             
[155] "Anas_acuta"                      "Anas_crecca"                    
[157] "Mergus_serrator"                 "Mergus_merganser"               
[159] "Bucephala_clangula"              "Melanitta_nigra"                
[161] "Somateria_mollissima"            "Callonetta_leucophrys"          
[163] "Branta_bernicla"                 "Branta_leucopsis"               
[165] "Anser_anser"                     "Cygnus_columbianus"             
[167] "Tadorna_tadorna"                 "Coturnix_japonica"              
[169] "Pucrasia_macrolopha"             "Phasianus_colchicus"            
[171] "Chrysolophus_pictus"             "Lophura_nycthemera"             
[173] "Lophura_ignita"                  "Syrmaticus_ellioti"             
[175] "Syrmaticus_reevesii"             "Perdix_perdix"                  
[177] "Tetrao_urogallus"                "Lagopus_muta"                   
[179] "Lagopus_lagopus"                 "Lophophorus_impejanus"          
[181] "Tragopan_temminckii"             "Pavo_cristatus"                 
[183] "Gallus_gallus"                   "Gallus_sonneratii"              
[185] "Rollulus_rouloul"                "Arborophila_torqueola"          
[187] "Numida_meleagris"               

setdiff(dat_organ_Bovidae$phylo, tree$tip.label)      # Database species absent in tree

character(0)

# Exclude mismatched species for consistency
tree_organ <- keep.tip(tree, intersect(tree$tip.label, dat_organ_Bovidae$phylo))
dat_organ_Bovidae <- dat_organ_Bovidae[dat_organ_Bovidae$phylo %in% tree_organ$tip.label, ]

# Re-check for mismatches after pruning
setdiff(tree_organ$tip.label, dat_organ_Bovidae$phylo)

character(0)

setdiff(dat_organ_Bovidae$phylo, tree_organ$tip.label)

character(0)

# Is ultrametric?
is.ultrametric(tree_organ)

[1] TRUE

# how many species?
length(tree_organ$tip.label)

[1] 17

# Compute phylogenetic covariance matrix
A_organ <- ape::vcv.phylo(tree_organ, corr = TRUE)

Model simple

model_simple_brain_Bovidae <- brm(
  log10_organ_size ~ 
    1 + 
    log10_body_size +
    (1 + log10_body_size | sex),
  data = dat_organ_Bovidae,
  family = gaussian(),
    prior = c(
    prior(normal(0.75, 0.5), class = "b", coef = "log10_body_size"),
    prior(normal(0, 2), class = "Intercept"),
    prior(student_t(3, 0, 0.5), class = "sd"),
    prior(student_t(3, 0, 1),   class = "sigma")
  ),
  seed = 6955,
  sample_prior = TRUE, 
  chains = 4, 
  cores = 4, 
  threads = threading(2),
  iter = 4000, 
  warmup = 2000,
  control = list(max_treedepth = 15,
                 adapt_delta = 0.99),
  save_pars = save_pars(all = TRUE),
  silent = TRUE, refresh = 0
)

Running MCMC with 4 parallel chains, with 2 thread(s) per chain...

Chain 2 finished in 13.7 seconds.
Chain 3 finished in 13.7 seconds.
Chain 1 finished in 20.0 seconds.
Chain 4 finished in 25.5 seconds.

All 4 chains finished successfully.
Mean chain execution time: 18.2 seconds.
Total execution time: 25.6 seconds.

Model check

pp_check(model_simple_brain_Bovidae)

Model summary

summary(model_simple_brain_Bovidae)

 Family: gaussian 
  Links: mu = identity; sigma = identity 
Formula: log10_organ_size ~ 1 + log10_body_size + (1 + log10_body_size | sex) 
   Data: dat_organ_Bovidae (Number of observations: 34) 
  Draws: 4 chains, each with iter = 4000; warmup = 2000; thin = 1;
         total post-warmup draws = 8000

Multilevel Hyperparameters:
~sex (Number of levels: 2) 
                               Estimate Est.Error l-95% CI u-95% CI Rhat
sd(Intercept)                      0.27      0.32     0.01     1.10 1.00
sd(log10_body_size)                0.13      0.19     0.00     0.62 1.00
cor(Intercept,log10_body_size)    -0.10      0.60    -0.98     0.94 1.00
                               Bulk_ESS Tail_ESS
sd(Intercept)                      2656     2965
sd(log10_body_size)                1421     2759
cor(Intercept,log10_body_size)     3888     3628

Regression Coefficients:
                Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept          -0.61      0.31    -1.33    -0.10 1.00     3725     3385
log10_body_size     0.57      0.11     0.26     0.78 1.00     1589     1271

Further Distributional Parameters:
      Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma     0.07      0.01     0.06     0.10 1.00     5645     4981

Draws were sampled using sample(hmc). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).

I will next extract, for each sex, the estimated slope and intercept, together with the 95% credible intervals.

# Extract combined coefficients (fixed + random)
coef(model_simple_brain_Bovidae)$sex %>%
{tibble(
  sex = dimnames(.)[[1]],
  intercept    = .[, "Estimate", "Intercept"],
  intercept_low  = .[, "Q2.5", "Intercept"], 
  intercept_high = .[, "Q97.5", "Intercept"]
)} %>%
bind_cols(
  tibble(
    sex = dimnames(coef(model_simple_brain_Bovidae)$sex)[[1]],
    slope = coef(model_simple_brain_Bovidae)$sex[, "Estimate", "log10_body_size"]
  ) %>% select(slope),
  tibble(
    sex = dimnames(coef(model_simple_brain_Bovidae)$sex)[[1]],
    slope_low  = coef(model_simple_brain_Bovidae)$sex[, "Q2.5", "log10_body_size"],
    slope_high = coef(model_simple_brain_Bovidae)$sex[, "Q97.5", "log10_body_size"]
  ) %>% select(slope_low, slope_high)
)

# A tibble: 2 × 7
  sex    intercept intercept_low intercept_high slope slope_low slope_high
  <chr>      <dbl>         <dbl>          <dbl> <dbl>     <dbl>      <dbl>
1 female    -0.564        -0.837         -0.298 0.585     0.530      0.641
2 male      -0.561        -0.832         -0.293 0.584     0.529      0.640

Model with phylogeny

model_phylo_brain_Bovidae <- brm(
  log10_organ_size ~ 
    1 + 
    log10_body_size +
    (1 + log10_body_size | sex) +
    (1 | gr(phylo, cov = A_organ)),
  data = dat_organ_Bovidae,
  data2 = list(A_organ = A_organ),
  family = gaussian(),
    prior = c(
    prior(normal(0.75, 0.5), class = "b", coef = "log10_body_size"),
    prior(normal(0, 2), class = "Intercept"),
    prior(student_t(3, 0, 0.5), class = "sd"),
    prior(student_t(3, 0, 1),   class = "sigma")
  ),
  seed = 6955,
  sample_prior = TRUE, 
  chains = 4, 
  cores = 4, 
  threads = threading(2),
  iter = 4000, 
  warmup = 2000,
  control = list(max_treedepth = 15,
                 adapt_delta = 0.99),
  save_pars = save_pars(all = TRUE),
  silent = TRUE, refresh = 0
)

Running MCMC with 4 parallel chains, with 2 thread(s) per chain...

Chain 1 finished in 37.8 seconds.
Chain 4 finished in 38.6 seconds.
Chain 3 finished in 43.9 seconds.
Chain 2 finished in 97.1 seconds.

All 4 chains finished successfully.
Mean chain execution time: 54.4 seconds.
Total execution time: 97.2 seconds.

Model check

pp_check(model_phylo_brain_Bovidae)

Model summary

summary(model_phylo_brain_Bovidae)

 Family: gaussian 
  Links: mu = identity; sigma = identity 
Formula: log10_organ_size ~ 1 + log10_body_size + (1 + log10_body_size | sex) + (1 | gr(phylo, cov = A_organ)) 
   Data: dat_organ_Bovidae (Number of observations: 34) 
  Draws: 4 chains, each with iter = 4000; warmup = 2000; thin = 1;
         total post-warmup draws = 8000

Multilevel Hyperparameters:
~phylo (Number of levels: 17) 
              Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept)     0.08      0.02     0.05     0.14 1.00     1575     2603

~sex (Number of levels: 2) 
                               Estimate Est.Error l-95% CI u-95% CI Rhat
sd(Intercept)                      0.24      0.29     0.00     0.98 1.00
sd(log10_body_size)                0.12      0.18     0.00     0.61 1.00
cor(Intercept,log10_body_size)    -0.07      0.62    -0.98     0.96 1.00
                               Bulk_ESS Tail_ESS
sd(Intercept)                      3083     3525
sd(log10_body_size)                1590     3350
cor(Intercept,log10_body_size)     5108     4908

Regression Coefficients:
                Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept          -0.50      0.32    -1.20     0.10 1.00     3586     4463
log10_body_size     0.55      0.11     0.25     0.74 1.00     1747     1526

Further Distributional Parameters:
      Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma     0.04      0.01     0.03     0.06 1.00     2113     2812

Draws were sampled using sample(hmc). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).

Phylogenetic signal

hyp <- paste(
  "sd_phylo__Intercept^2 /",
  "(sd_phylo__Intercept^2 + sd_sex__Intercept^2 + sigma^2) = 0"
)
(hyp <- hypothesis(model_phylo_brain_Bovidae, hyp, class = NULL))

Hypothesis Tests for class :
                Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
1 (sd_phylo__Interc... = 0     0.32      0.29     0.01     0.88       0.61
  Post.Prob Star
1      0.38    *
---
'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
'*': For one-sided hypotheses, the posterior probability exceeds 95%;
for two-sided hypotheses, the value tested against lies outside the 95%-CI.
Posterior probabilities of point hypotheses assume equal prior probabilities.

lambda_brain <- hyp$hypothesis$Estimate

I will next extract, for each sex, the estimated slope and intercept, together with the 95% credible intervals.

# Extract combined coefficients (fixed + random)
coef(model_phylo_brain_Bovidae)$sex %>%
{tibble(
  sex = dimnames(.)[[1]],
  intercept    = .[, "Estimate", "Intercept"],
  intercept_low  = .[, "Q2.5", "Intercept"], 
  intercept_high = .[, "Q97.5", "Intercept"]
)} %>%
bind_cols(
  tibble(
    sex = dimnames(coef(model_phylo_brain_Bovidae)$sex)[[1]],
    slope = coef(model_phylo_brain_Bovidae)$sex[, "Estimate", "log10_body_size"]
  ) %>% select(slope),
  tibble(
    sex = dimnames(coef(model_phylo_brain_Bovidae)$sex)[[1]],
    slope_low  = coef(model_phylo_brain_Bovidae)$sex[, "Q2.5", "log10_body_size"],
    slope_high = coef(model_phylo_brain_Bovidae)$sex[, "Q97.5", "log10_body_size"]
  ) %>% select(slope_low, slope_high)
)

# A tibble: 2 × 7
  sex    intercept intercept_low intercept_high slope slope_low slope_high
  <chr>      <dbl>         <dbl>          <dbl> <dbl>     <dbl>      <dbl>
1 female    -0.486        -0.895        -0.0279 0.568     0.477      0.651
2 male      -0.475        -0.873        -0.0117 0.566     0.474      0.646

Model comparison

loo_simple <- loo(model_simple_brain_Bovidae)
loo_phylo <- loo(model_phylo_brain_Bovidae)
loo_compare(loo_simple, loo_phylo)

                           elpd_diff se_diff
model_phylo_brain_Bovidae    0.0       0.0  
model_simple_brain_Bovidae -11.2       3.3  

Extract coefficients (among others things) for all models

The next task is to extract the coefficients from all models (8) in order to prepare a table (Table S2 in the paper) that presents the coefficients by sex, global coefficients. Additionally, I will include the Pagel’s \(\lambda\) representing the phylogenetic signal.

# list of models (no brain included, for now)
models_list_simple <- list(
  model_simple_liver,
  model_simple_heart,
  model_simple_pituitary_glands,
  model_simple_spleen,
  model_simple_stomach,
  model_simple_lungs,
  model_simple_adrenal_glands,
  model_simple_kidneys
)

models_list_phylo <- list(
  model_phylo_liver,
  model_phylo_heart,
  model_phylo_pituitary_glands,
  model_phylo_spleen,
  model_phylo_stomach,
  model_phylo_lungs,
  model_phylo_adrenal_glands,
  model_phylo_kidneys
)

# Organ names for simple models
names(models_list_simple) <- c(
  "liver","heart","pituitary_glands","spleen",
  "stomach","lungs","adrenal_glands","kidneys"
)

# Organ names for phylogenetic models
names(models_list_phylo) <- c(
  "liver","heart","pituitary_glands","spleen",
  "stomach","lungs","adrenal_glands","kidneys"
)

# Hypothesis string for lambda (phylogenetic signal), based on the vignette
# available here:
# https://cran.r-project.org/web/packages/brms/vignettes/brms_phylogenetics.html

hyp_lambda <- paste0(
  "sd_phylo__Intercept^2 /",
  "(sd_phylo__Intercept^2 + sd_sex__Intercept^2 + sigma^2) = 0"
)

# Make a function to do the process less repetitive. It will extract from each
# model sex-specific coefficients + global slope + lambda (for phylo models only)

extract_all_coefs <- function(fit, organ, model_type) {
  # Sex-specific coefficients (random effects)
  coef_sex <- coef(fit)$sex %>%
    as_tibble(rownames = "sex") %>%
    select(sex, matches("Estimate|Q2.5|Q97.5")) %>%
    transmute(
      model_type,
      organ,
      sex,
      intercept      = Estimate.Intercept,
      intercept_low  = Q2.5.Intercept,
      intercept_high = Q97.5.Intercept,
      slope          = Estimate.log10_body_size,
      slope_low      = Q2.5.log10_body_size,
      slope_high     = Q97.5.log10_body_size
    )
  
  # Global slope (fixed effect)
  global_slope_vec <- fixef(fit)["log10_body_size", ]
  global_slope <- tibble(
    global_slope      = global_slope_vec["Estimate"],
    global_slope_low  = global_slope_vec["Q2.5"],
    global_slope_high = global_slope_vec["Q97.5"]
  )
  
  # Lambda (phylogenetic signal) - only for phylo models
  if(model_type == "phylo") {
    hyp_lambda <- hypothesis(fit, hyp_lambda, class = NULL)
    lambda_vals <- hyp_lambda$hypothesis %>%
      transmute(
        lambda         = Estimate
      )
  } else {
    lambda_vals <- tibble(lambda = NA_real_)
  }
  
  # Combine everything
  coef_sex %>%
    bind_cols(global_slope, lambda_vals)
}

# Create complete data frames
df_simple_all_organs <- imap_dfr(
  models_list_simple,
  ~ extract_all_coefs(.x, organ = .y, model_type = "simple")
)

df_phylo_all_organs <- imap_dfr(
  models_list_phylo,
  ~ extract_all_coefs(.x, organ = .y, model_type = "phylo")
)

# Final data frame with everything
df_all_organs <- bind_rows(df_simple_all_organs, df_phylo_all_organs)

# add R²
r2_simple <- imap(models_list_simple, ~ bayes_R2(.x)["R2", "Estimate"])
r2_phylo  <- imap(models_list_phylo,  ~ bayes_R2(.x)["R2", "Estimate"])

df_all_organs <- df_all_organs %>%
  arrange(model_type,organ) %>%
  mutate(R2 = case_when(
    model_type == "simple" ~ r2_simple[organ],
    model_type == "phylo"  ~ r2_phylo[organ]
  ))

Table S2

df_all_organs_ci <- df_all_organs %>%
  mutate(
    lambda = as.numeric(lambda),
    R2 = as.numeric(R2),
    intercept_ci    = sprintf("%.2f [%.2f, %.2f]", 
                              round(intercept, 2), round(intercept_low, 2), round(intercept_high, 2)),
    slope_ci        = sprintf("%.2f [%.2f, %.2f]", 
                              round(slope, 2), round(slope_low, 2), round(slope_high, 2)),
    global_slope_ci = sprintf("%.2f [%.2f, %.2f]", 
                              round(global_slope, 2), round(global_slope_low, 2), round(global_slope_high, 2)),
    lambda = sprintf("%.2f", round(lambda, 2)),
    R2 = sprintf("%.2f", round(R2, 2))
  ) %>%
  mutate(across(where(is.list), as.character)) %>%
  select(model_type, organ, sex, intercept_ci, slope_ci, global_slope_ci, lambda, R2) %>%
  arrange(organ) %>%
  as.data.frame(stringsAsFactors = FALSE)

# Table with filters
df_all_organs_ci %>%
  datatable(
    filter = 'top',
    options = list(
      columnDefs = list(
        list(width = "5%", targets = 0),
        list(width = "15%", targets = 1), 
        list(width = "7%", targets = 2),
        list(width = "17%", targets = 3),
        list(width = "17%", targets = 4),
        list(width = "17%", targets = 5),
        list(width = "7%", targets = 6),
        list(width = "7%", targets = 7)
      ),
      pageLength = 25,
      scrollX = TRUE,
      autoWidth = FALSE
    ),
    class = 'cell-border stripe hover',
    escape = FALSE
  ) %>%
  formatStyle(columns = 0:7, borderRight = "1px solid #ddd")

Figure 2

What I will do here is copy the list of simple and phylogenetic models, their names, and extract the LOO values. Then, I will compare these using the loo_compare function, extract the estimates from this comparison, and plot them.

# Define model lists
models_list_simple <- list(
  model_simple_liver, model_simple_heart, model_simple_pituitary_glands,
  model_simple_spleen, model_simple_stomach, model_simple_lungs,
  model_simple_adrenal_glands, model_simple_kidneys
)

names(models_list_simple) <- c(
  "liver", "heart", "pituitary_glands", "spleen",
  "stomach", "lungs", "adrenal_glands", "kidneys"
)

names(models_list_phylo) <- names(models_list_simple)

# Compare models and extract elpd_diff + se
diff_by_organ <- map_dfr(names(models_list_simple), function(org) {

  # 1. Calcular LOO
  loo_phylo  <- loo(models_list_phylo[[org]])
  loo_simple <- loo(models_list_simple[[org]])

  # 2. Comparar
  comp <- loo_compare(loo_phylo, loo_simple)
  comp_df <- as.data.frame(comp)

  # 3. Extraer fila NO referencia (modelo simple)
  row <- comp_df[comp_df$elpd_diff != 0, , drop = FALSE]

  # Seguridad (debería ser exactamente 1 fila)
  if (nrow(row) != 1) {
    stop("Unexpected loo_compare output for organ: ", org)
  }

  # 4. Construir salida
  tibble(
    organ     = gsub("_", " ", org),
    diff_elpd = -row$elpd_diff,   # phylo − simple
    se_diff   =  row$se_diff,
    Vetahri_score   = abs((-row$elpd_diff) / row$se_diff)
  )
}) %>%
  mutate(
    sig_level = if_else(Vetahri_score > 4, "large", "ns")
  ) %>%
  arrange(desc(diff_elpd))


# Figure 2
Figure_2a <- ggplot(diff_by_organ, aes(x = reorder(organ, diff_elpd), y = diff_elpd, 
                                colour = sig_level)) +
  geom_point(size = 3) +
  geom_errorbar(aes(ymin = diff_elpd - se_diff, ymax = diff_elpd + se_diff),
                width = 0.3, linewidth = 0.8) +
  coord_flip() +
scale_colour_manual(
  values = c("ns" = "grey30", "large" = "#009E73"),
  name = "Model improvement",
  labels = c("ns" = expression(z <= 4), "large" = expression(z > 4))
) +
labs(
  x = NULL, 
  y = expression(Delta ~ "ELPD" ~ "(phylogenetic - simple)")
  ) +
  theme_pubr(base_size = 12) +
  theme(
    panel.grid.minor = element_blank(),
    axis.text.y  = element_text(size = 12),
    axis.title.y = element_text(size = 12),
    legend.position = c(0.85, 0.15),
    legend.margin = margin(3, 3, 3, 3),
    legend.box.just = "left",
    legend.title = element_text(size = 10)
  )

Figure_2a

# list of models (only brain)
models_list_simple_brain <- list(
  model_simple_brain_Cichlidae,
  model_simple_brain_Syngnathidae,
  model_simple_brain_Psittacidae,
  model_simple_brain_Fringillidae,
  model_simple_brain_Phasianidae,
  model_simple_brain_Anatidae,
  model_simple_brain_Cercopithecidae,
  model_simple_brain_Bovidae
)

models_list_phylo_brain <- list(
  model_phylo_brain_Cichlidae,
  model_phylo_brain_Syngnathidae,
  model_phylo_brain_Psittacidae,
  model_phylo_brain_Fringillidae,
  model_phylo_brain_Phasianidae,
  model_phylo_brain_Anatidae,
  model_phylo_brain_Cercopithecidae,
  model_phylo_brain_Bovidae
)

# family names for simple models
names(models_list_simple_brain) <- c(
  "Cichlidae","Syngnathidae","Psittacidae","Fringillidae",
  "Phasianidae","Anatidae","Cercopithecidae","Bovidae"
)

# Organ names for phylogenetic models
names(models_list_phylo_brain) <- names(models_list_simple_brain)

# Compare models and extract elpd_diff + se
diff_by_family <- map_dfr(names(models_list_simple_brain), function(fam) {

  # 1. Calcular LOO
  loo_phylo_brain  <- loo(models_list_phylo_brain[[fam]])
  loo_simple_brain <- loo(models_list_simple_brain[[fam]])

  # 2. Comparar
  comp <- loo_compare(loo_phylo_brain, loo_simple_brain)
  comp_df_brain <- as.data.frame(comp)

  # 3. Extraer fila NO referencia (modelo simple)
  row <- comp_df_brain[comp_df_brain$elpd_diff != 0, , drop = FALSE]

  # Seguridad (debería ser exactamente 1 fila)
  if (nrow(row) != 1) {
    stop("Unexpected loo_compare output for organ: ", fam)
  }

  # 4. Construir salida
  tibble(
    family     = gsub("_", " ", fam),
    diff_elpd = -row$elpd_diff,   # phylo − simple
    se_diff   =  row$se_diff,
    Vetahri_score   = abs((-row$elpd_diff) / row$se_diff)
  )
}) %>%
  mutate(
    sig_level = if_else(Vetahri_score > 4, "large", "ns")
  ) %>%
  arrange(desc(diff_elpd))


Figure_2b <- ggplot(diff_by_family, aes(x = reorder(family, diff_elpd), y = diff_elpd, 
                                colour = sig_level)) +
  geom_point(size = 3) +
  geom_errorbar(aes(ymin = diff_elpd - se_diff, ymax = diff_elpd + se_diff),
                width = 0.3, linewidth = 0.8) +
  coord_flip() +
scale_colour_manual(
  values = c("ns" = "grey30", "large" = "#009E73"),
  name = "Model improvement",
  labels = c("ns" = expression(z <= 4), "large" = expression(z > 4))
) +
labs(
  x = NULL, 
  y = expression(Delta ~ "ELPD" ~ "(phylogenetic - simple)")
  ) +
  theme_pubr(base_size = 12) +
  theme(
    panel.grid.minor = element_blank(),
    axis.text.y  = element_text(size = 12),
    axis.title.y = element_text(size = 12),
    legend.position = c(0.85, 0.15),
    legend.margin = margin(3, 3, 3, 3),
    legend.box.just = "left",
    legend.title = element_text(size = 10)
  )

Figure_2b

Figure_2 <- plot_grid(Figure_2a, Figure_2b, 
                     labels = c("A", "B"),
                     ncol = 1,  
                     align = "hv")

# Export figure
ggsave("../outputs/Figure_2.pdf", Figure_2, width = 5, height = 7)

Figure 3

This figure comprises four plots. Two of these depict the relationships between slopes and intercepts for males and females derived from phylogenetic models. The other two present similar information but based on simple models (without phylogenetic information). Displaying slopes and intercepts from both model types was pragmatic, as the importance of accounting for phylogeny varies by organ—some require it, while others show phylogenetic contributions comparable to excluding it.

# Define common theme (used by all plots)
common_theme <- theme_bw() +
  theme(
    panel.grid.major = element_blank(),
    panel.grid.minor = element_blank(),
    legend.position = c(0.15, 0.85),
    legend.key.size = unit(0.4, "cm"),
    legend.text = element_text(size = 8),
    legend.title = element_blank(),
    legend.spacing.y = unit(0.5, "cm"),
    legend.margin = margin(2, 2, 2, 2),
    legend.background = element_rect(fill = "white", size = 0.3),
    plot.margin = margin(15, 15, 15, 15),
    axis.text = element_text(size = 12),
    axis.title = element_text(size = 12),
    axis.title.x = element_text(margin = margin(t = 12)),
    axis.title.y = element_text(margin = margin(r = 5)),
    panel.border = element_rect(colour = "black", fill = NA, size = 1)
  )

# Define legend theme
no_legend_theme <- theme_bw() +
  theme(
    panel.grid = element_blank(),
    legend.position = "left",
    plot.margin = margin(15, 15, 15, 15),
    axis.text = element_text(size = 12),
    axis.title = element_text(size = 12),
    axis.title.x = element_text(margin = margin(t = 12)),
    axis.title.y = element_text(margin = margin(r = 5)),
    panel.border = element_rect(colour = "black", fill = NA, size = 1)
  )

# Clean organ names and colours
df_all_organs$organ <- gsub("_", " ", df_all_organs$organ)
all_organs <- sort(unique(df_all_organs$organ))
my_cols <- setNames(c("#4169E1", "#DC143C", "#D1600F", "#8B0000", 
                      "#FFFF00", "#8DA715", "#FF69B4", "black"),
                    all_organs)

# Plot 1: slopes - phylogenetic model (with legend)
df1 <- df_all_organs %>% 
  filter(model_type == "phylo", sex %in% c("male", "female")) %>%
  select(organ, sex, slope, slope_low, slope_high) %>%
  pivot_wider(names_from = sex, values_from = c(slope, slope_low, slope_high), names_sep = "_") %>%
  mutate(male_xmin = slope_low_male, male_xmax = slope_high_male,
         female_ymin = slope_low_female, female_ymax = slope_high_female)

p1 <- ggplot(df1, aes(x = slope_male, y = slope_female)) +
  geom_errorbarh(aes(xmin = male_xmin, xmax = male_xmax, colour = organ), height = 0.038, size = 0.8) +
  geom_errorbar(aes(ymin = female_ymin, ymax = female_ymax, colour = organ), width = 0.038, size = 0.8) +
  geom_point(aes(fill = organ), size = 2.8, shape = 21, stroke = 0.6, colour = "white") +
  geom_abline(intercept = 0, slope = 1, linetype = "dashed", colour = "grey40", size = 0.6, alpha = 0.5) +
  scale_colour_manual(values = my_cols) +
  scale_fill_manual(values = my_cols, guide = "none") +
  guides(colour = guide_legend(
    override.aes = list(shape = 21, colour = "white", stroke = 0.6, size = 3))) +
  labs(x = "Male slope", y = "Female slope") +
  coord_fixed() + common_theme +
  scale_x_continuous(limits = c(0, 1.5), breaks = seq(0, 1.5, by = 0.3)) +
  scale_y_continuous(limits = c(0, 1.5), breaks = seq(0, 1.5, by = 0.3))

# Plot 2: slopes - simple model
df2 <- df_all_organs %>% 
  filter(model_type == "simple", sex %in% c("male", "female")) %>%
  select(organ, sex, slope, slope_low, slope_high) %>%
  pivot_wider(names_from = sex, values_from = c(slope, slope_low, slope_high), names_sep = "_") %>%
  mutate(male_xmin = slope_low_male, male_xmax = slope_high_male,
         female_ymin = slope_low_female, female_ymax = slope_high_female)

p2 <- ggplot(df2, aes(x = slope_male, y = slope_female)) +
  geom_errorbarh(aes(xmin = male_xmin, xmax = male_xmax, colour = organ), height = 0.038, size = 0.8) +
  geom_errorbar(aes(ymin = female_ymin, ymax = female_ymax, colour = organ), width = 0.038, size = 0.8) +
  geom_point(aes(fill = organ), size = 2.8, shape = 21, stroke = 0.6, colour = "white") +
  geom_abline(intercept = 0, slope = 1, linetype = "dashed", colour = "grey40", size = 0.6, alpha = 0.5) +
  scale_colour_manual(values = my_cols, guide = "none") +
  scale_fill_manual(values = my_cols, guide = "none") +
  labs(x = "Male slope", y = "") +
  coord_fixed() + no_legend_theme +
  scale_x_continuous(limits = c(0, 1.5), breaks = seq(0, 1.5, by = 0.3)) +
  scale_y_continuous(limits = c(0, 1.5), breaks = seq(0, 1.5, by = 0.3))

# Plot 3: intercepts - phylogenetic model
df3 <- df_all_organs %>% 
  filter(model_type == "phylo", sex %in% c("male", "female")) %>%
  select(organ, sex, intercept, intercept_low, intercept_high) %>%
  pivot_wider(names_from = sex, values_from = c(intercept, intercept_low, intercept_high), names_sep = "_") %>%
  mutate(male_xmin = intercept_low_male, male_xmax = intercept_high_male,
         female_ymin = intercept_low_female, female_ymax = intercept_high_female)

p3 <- ggplot(df3, aes(x = intercept_male, y = intercept_female)) +
  geom_errorbarh(aes(xmin = male_xmin, xmax = male_xmax, colour = organ), height = 0.12, size = 0.8) +
  geom_errorbar(aes(ymin = female_ymin, ymax = female_ymax, colour = organ), width = 0.12, size = 0.8) +
  geom_point(aes(fill = organ), size = 2.8, shape = 21, stroke = 0.6, colour = "white") +
  geom_abline(intercept = 0, slope = 1, linetype = "dashed", colour = "grey40", size = 0.6, alpha = 0.5) +
  scale_colour_manual(values = my_cols, guide = "none") +
  scale_fill_manual(values = my_cols, guide = "none") +
  labs(x = "Male intercept", y = "Female intercept") +
  coord_fixed() + no_legend_theme +
  scale_x_continuous(limits = c(-5, 0), breaks = seq(-5, 0, by = 1)) +
  scale_y_continuous(limits = c(-5, 0), breaks = seq(-5, 0, by = 1))

# Plot 4: intercepts - simple model
df4 <- df_all_organs %>% 
  filter(model_type == "simple", sex %in% c("male", "female")) %>%
  select(organ, sex, intercept, intercept_low, intercept_high) %>%
  pivot_wider(names_from = sex, values_from = c(intercept, intercept_low, intercept_high), names_sep = "_") %>%
  mutate(male_xmin = intercept_low_male, male_xmax = intercept_high_male,
         female_ymin = intercept_low_female, female_ymax = intercept_high_female)

p4 <- ggplot(df4, aes(x = intercept_male, y = intercept_female)) +
  geom_errorbarh(aes(xmin = male_xmin, xmax = male_xmax, colour = organ), height = 0.12, size = 0.8) +
  geom_errorbar(aes(ymin = female_ymin, ymax = female_ymax, colour = organ), width = 0.12, size = 0.8) +
  geom_point(aes(fill = organ), size = 2.8, shape = 21, stroke = 0.6, colour = "white") +
  geom_abline(intercept = 0, slope = 1, linetype = "dashed", colour = "grey40", size = 0.6, alpha = 0.5) +
  scale_colour_manual(values = my_cols, guide = "none") +
  scale_fill_manual(values = my_cols, guide = "none") +
  labs(x = "Male intercept", y = "") +
  coord_fixed() + no_legend_theme +
  scale_x_continuous(limits = c(-5, 0), breaks = seq(-5, 0, by = 1)) +
  scale_y_continuous(limits = c(-5, 0), breaks = seq(-5, 0, by = 1))

# temporal plot
legend_plot <- ggplot(df1, aes(x = 1, y = 1, fill = organ)) +
  geom_point(shape = 21, size = 4, stroke = 0.8, colour = "white") +
  scale_fill_manual(values = my_cols) +
  theme_void() +
  guides(fill = guide_legend(title = NULL, override.aes = list(shape = 21, colour = "white", stroke = 0.6, size = 3))) +
  theme(legend.position = "right", legend.spacing.y = unit(0.3, "cm"))

# Extract legend from plot from the previous plot
legend_right <- get_legend(legend_plot+ theme(legend.position = "right", legend.spacing.y = unit(0.3, "cm")))

# Add model labels to panels
p1 <- p1 + theme(legend.position = "none", plot.margin = margin(2, 2, 2, 2)) +
  annotate("text", x = 0.75, y = 1.5, label = "Phylogenetic model", size = 4, hjust = 0.5, vjust = 0.5, colour = "black")

p2 <- p2 + theme(legend.position = "none", plot.margin = margin(2, 2, 2, 2)) +
  annotate("text", x = 0.75, y = 1.5, label = "Simple model", size = 4, hjust = 0.5, vjust = 0.5, colour = "black")

p3 <- p3 + theme(legend.position = "none", plot.margin = margin(2, 2, 2, 2)) +
  annotate("text", x = -2.5, y = 0, label = "Phylogenetic model", size = 4, hjust = 0.5, vjust = 0.5, colour = "black")

p4 <- p4 + theme(legend.position = "none", plot.margin = margin(2, 2, 2, 2)) +
  annotate("text", x = -2.5, y = 0, label = "Simple model", size = 4, hjust = 0.5, vjust = 0.5, colour = "black")

# Combine panels and create final figure
combined_plot <- (p1 | p2) / (p3 | p4) + plot_layout(widths = c(1, 1), heights = c(1, 1))

Figure_3 <- plot_grid(combined_plot, legend_right, rel_widths = c(4, 1))

# Export high-resolution figure
ggsave("../outputs/Figure_3.png", Figure_3, width = 8, height = 7, dpi = 1200)
ggsave("../outputs/Figure_3.pdf", Figure_3, width = 8, height = 7)

Extract coefficients from brain models

# Hypothesis string for lambda (phylogenetic signal), based on the vignette
# available here:
# https://cran.r-project.org/web/packages/brms/vignettes/brms_phylogenetics.html

hyp_lambda <- paste0(
  "sd_phylo__Intercept^2 /",
  "(sd_phylo__Intercept^2 + sd_sex__Intercept^2 + sigma^2) = 0"
)

# Make a function to do the process less repetitive. It will extract from each
# model sex-specific coefficients + global slope + lambda (for phylo models only)
extract_all_coefs <- function(fit, family, model_type) {
  # Sex-specific coefficients (random effects)
  coef_sex <- coef(fit)$sex %>%
    as_tibble(rownames = "sex") %>%
    select(sex, matches("Estimate|Q2.5|Q97.5")) %>%
    transmute(
      model_type,
      family,
      sex,
      intercept      = Estimate.Intercept,
      intercept_low  = Q2.5.Intercept,
      intercept_high = Q97.5.Intercept,
      slope          = Estimate.log10_body_size,
      slope_low      = Q2.5.log10_body_size,
      slope_high     = Q97.5.log10_body_size
    )
  
  # Global slope (fixed effect)
  global_slope_vec <- fixef(fit)["log10_body_size", ]
  global_slope <- tibble(
    global_slope      = global_slope_vec["Estimate"],
    global_slope_low  = global_slope_vec["Q2.5"],
    global_slope_high = global_slope_vec["Q97.5"]
  )
  
  # Lambda (phylogenetic signal) - only for phylo models
  if(model_type == "phylo") {
    hyp_lambda <- hypothesis(fit, hyp_lambda, class = NULL)
    lambda_vals <- hyp_lambda$hypothesis %>%
      transmute(
        lambda         = Estimate
      )
  } else {
    lambda_vals <- tibble(lambda = NA_real_)
  }
  
  # Combine everything
  coef_sex %>%
    bind_cols(global_slope, lambda_vals)
}

# Create complete data frames
df_simple_all_family <- imap_dfr(
  models_list_simple_brain,
  ~ extract_all_coefs(.x, family = .y, model_type = "simple")
)

df_phylo_all_family<- imap_dfr(
  models_list_phylo_brain,
  ~ extract_all_coefs(.x, family = .y, model_type = "phylo")
)

# Final data frame with everything
df_all_family <- bind_rows(df_simple_all_family, df_phylo_all_family)

# add R²
r2_simple <- imap(models_list_simple_brain, ~ bayes_R2(.x)["R2", "Estimate"])
r2_phylo  <- imap(models_list_phylo_brain,  ~ bayes_R2(.x)["R2", "Estimate"])

df_all_family <- df_all_family %>%
  arrange(model_type,family) %>%
  mutate(R2 = case_when(
    model_type == "simple" ~ r2_simple[family],
    model_type == "phylo"  ~ r2_phylo[family]
  ))

Table S3

df_all_family <- df_all_family %>%
  mutate(
    lambda = as.numeric(lambda),
    R2 = as.numeric(R2),
    intercept_ci    = sprintf("%.2f [%.2f, %.2f]", 
                              round(intercept, 2), round(intercept_low, 2), round(intercept_high, 2)),
    slope_ci        = sprintf("%.2f [%.2f, %.2f]", 
                              round(slope, 2), round(slope_low, 2), round(slope_high, 2)),
    global_slope_ci = sprintf("%.2f [%.2f, %.2f]", 
                              round(global_slope, 2), round(global_slope_low, 2), round(global_slope_high, 2)),
    lambda = sprintf("%.2f", round(lambda, 2)),
    R2 = sprintf("%.2f", round(R2, 2))
  ) %>%
  mutate(across(where(is.list), as.character)) %>%
  select(model_type, family, sex, intercept_ci, slope_ci, global_slope_ci, lambda, R2) %>%
  arrange(family) %>%
  as.data.frame(stringsAsFactors = FALSE)

# Table with filters remains identical
df_all_family %>%
  datatable(
    filter = 'top',
    options = list(
      columnDefs = list(
        list(width = "5%", targets = 0),
        list(width = "15%", targets = 1), 
        list(width = "7%", targets = 2),
        list(width = "17%", targets = 3),
        list(width = "17%", targets = 4),
        list(width = "17%", targets = 5),
        list(width = "7%", targets = 6),
        list(width = "7%", targets = 7)
      ),
      pageLength = 25,
      scrollX = TRUE,
      autoWidth = FALSE
    ),
    class = 'cell-border stripe hover',
    escape = FALSE
  ) %>%
  formatStyle(columns = 0:7, borderRight = "1px solid #ddd")

Figure 4

models_list_phylo_brain <- list(
  model_phylo_brain_Cichlidae,
  model_phylo_brain_Syngnathidae,
  model_phylo_brain_Psittacidae,
  model_phylo_brain_Fringillidae,
  model_phylo_brain_Phasianidae,
  model_phylo_brain_Anatidae,
  model_phylo_brain_Cercopithecidae,
  model_phylo_brain_Bovidae
)

family_names <- c("Cichlidae", "Syngnathidae", "Psittacidae", "Fringillidae", 
                  "Phasianidae", "Anatidae", "Cercopithecidae",  "Bovidae")

sex_colours <- c("male" = "#FF0000A0", "female" = "#1F78B4", "Grand mean" = "gray70")

common_theme <- theme_bw(base_size = 12) +
  theme(
    panel.grid.major = element_blank(),
    panel.grid.minor = element_blank(),
    legend.position = "none",
    panel.spacing.x = unit(0.3, "lines"),
    axis.text.y = element_blank(),       
    axis.text.x = element_text(size = 12),
    axis.title.x = element_text(margin = margin(t = 8)),
    axis.title.y = element_text(margin = margin(r = 8)),
    axis.title = element_text(size = 14),
    plot.margin = margin(t = 4, r = 8, b = 4, l = 8, unit = "pt")
  )

plot_slopes <- function(model, family_name) {
  fixed_effects <- model %>% spread_draws(b_log10_body_size)
  random_slopes <- model %>% 
    gather_draws(r_sex[sex, term], regex = TRUE) %>% 
    filter(term == "log10_body_size")
  
  slope_draws <- random_slopes %>%
    left_join(fixed_effects, by = ".draw") %>%
    mutate(slope = .value + b_log10_body_size, sex_label = glue::glue("{sex}")) %>%
    select(.draw, sex_label, slope)
  
  global_slope_draws <- fixed_effects %>%
    mutate(slope = b_log10_body_size, sex_label = "Grand mean") %>%
    select(.draw, sex_label, slope)
  
  slope_draws_combined <- bind_rows(slope_draws, global_slope_draws)
  slope_draws_combined$sex_label <- factor(
    slope_draws_combined$sex_label,
    levels = c(sort(unique(slope_draws$sex_label)), "Grand mean")
  )
  
  ggplot(slope_draws_combined, aes(x = slope, y = sex_label, fill = sex_label)) +
    annotate("rect", 
             xmin = -0.6, xmax = 1.6, 
             ymin = 3.69, ymax = 3.99,
             fill = 'grey90', color = NA) +
    annotate("text", 
             x = 0.5, y = 3.85,
             label = family_name,
             size = 4.5, fontface = "bold",
             hjust = 0.5, vjust = 0.5) +
    stat_halfeye(aes(x = slope), scale = 0.8, justification = 0.08) +
    scale_y_discrete(expand = expansion(mult = c(0.02, 0.35))) +  
    coord_cartesian(xlim = c(-0.5, 1.5), clip = "off") +
    scale_fill_manual(values = sex_colours) +
    labs(x = "", y = NULL, title = NULL) + 
    common_theme
}

plot_intercepts <- function(model, family_name) {
  fixed_effects <- model %>% spread_draws(b_Intercept)
  random_intercepts <- model %>% 
    gather_draws(r_sex[sex, term], regex = TRUE) %>% 
    filter(term == "Intercept")
  
  intercept_draws <- random_intercepts %>%
    left_join(fixed_effects, by = c(".chain", ".iteration", ".draw")) %>%
    mutate(intercept = .value + b_Intercept, sex_label = glue::glue("{sex}")) %>%
    select(.draw, sex_label, intercept)
  
  global_intercept_draws <- fixed_effects %>%
    mutate(intercept = b_Intercept, sex_label = "Grand mean") %>%
    select(.draw, sex_label, intercept)
  
  intercept_draws_combined <- bind_rows(intercept_draws, global_intercept_draws)
  intercept_draws_combined$sex_label <- factor(
    intercept_draws_combined$sex_label,
    levels = c(sort(unique(intercept_draws$sex_label)), "Grand mean")
  )
  
  ggplot(intercept_draws_combined, aes(x = intercept, y = sex_label, fill = sex_label)) +
  annotate(
    "rect",
    xmin = -Inf, xmax = Inf,
    ymin = 3.69, ymax = 3.99,
    fill = "grey90", color = NA
  ) +
  annotate(
    "text",
    x = 0, y = 3.85,
    label = family_name,
    size = 4.5, fontface = "bold",
    hjust = 0.5, vjust = 0.5
  ) +
  stat_halfeye(scale = 0.8, justification = 0.08) +
  scale_x_continuous(breaks = seq(-3, 3, 1.5)) +
  scale_y_discrete(expand = expansion(mult = c(0.02, 0.35))) +
  coord_cartesian(xlim = c(-3.2, 3.2), clip = "off") +
  scale_fill_manual(values = sex_colours) +
  labs(x = "", y = NULL) +
  common_theme
}

# make PLOTS
intercept_plots <- map2(models_list_phylo_brain, family_names, plot_intercepts)
slope_plots <- map2(models_list_phylo_brain, family_names, plot_slopes)

Figure_4_intercepts <- plot_grid(
  plotlist = intercept_plots,
  ncol = 2,
  align = "hv",
  rel_heights = rep(1, 4)
)

Figure_4_slopes <- plot_grid(
  plotlist = slope_plots,
  ncol = 2,
  align = "hv",
  rel_heights = rep(1, 4)
)

Figure_4 <- plot_grid(
  Figure_4_intercepts,
  Figure_4_slopes,
  ncol = 2,
  rel_widths = c(1, 1),
  align = "hv"
)

ggsave("../outputs/Figure_4.png", Figure_4, width = 14, height = 13, dpi = 1200)
ggsave("../outputs/Figure_4.pdf", Figure_4, width = 14, height = 13)

Session information

R version 4.3.2 (2023-10-31)

Platform: aarch64-apple-darwin20 (64-bit)

attached base packages: stats, graphics, grDevices, utils, datasets, methods and base

other attached packages: rstan(v.2.32.7), StanHeaders(v.2.32.10), ggtreeExtra(v.1.12.0), ggnewscale(v.0.5.2), DT(v.0.33), ggridges(v.0.5.6), RColorBrewer(v.1.1-3), modelr(v.0.1.11), broom(v.1.0.8), viridis(v.0.6.5), viridisLite(v.0.4.2), posterior(v.1.6.1), lubridate(v.1.9.4), forcats(v.1.0.0), readr(v.2.1.5), tidyverse(v.2.0.0), furrr(v.0.3.1), future(v.1.40.0), cmdstanr(v.0.9.0), purrr(v.1.0.4), loo(v.2.8.0), bayestestR(v.0.16.1), tidybayes(v.3.0.7), bayesplot(v.1.13.0), dplyr(v.1.1.4), brms(v.2.22.0), Rcpp(v.1.1.0), tidyr(v.1.3.1), stringr(v.1.5.1), details(v.0.4.0), ggthemes(v.5.1.0), tibble(v.3.2.1), ggtree(v.3.10.1), patchwork(v.1.3.0), cowplot(v.1.1.3), ggpubr(v.0.6.0), ggplot2(v.3.5.2), kableExtra(v.1.4.0), readxl(v.1.4.5), phytools(v.2.4-4), maps(v.3.4.3), ape(v.5.8-1) and knitr(v.1.50)

loaded via a namespace (and not attached): svUnit(v.1.0.6), ggplotify(v.0.1.2), cellranger(v.1.1.0), lifecycle(v.1.0.4), rstatix(v.0.7.2), doParallel(v.1.0.17), globals(v.0.17.0), processx(v.3.8.6), lattice(v.0.22-7), MASS(v.7.3-60), insight(v.1.3.1), crosstalk(v.1.2.1), ggdist(v.3.3.3), backports(v.1.5.0), magrittr(v.2.0.3), sass(v.0.4.10), rmarkdown(v.2.29), jquerylib(v.0.1.4), yaml(v.2.3.10), pkgbuild(v.1.4.8), abind(v.1.4-8), expm(v.1.0-0), quadprog(v.1.5-8), yulab.utils(v.0.2.0), tensorA(v.0.36.2.1), inline(v.0.3.21), listenv(v.0.9.1), tidytree(v.0.4.6), bridgesampling(v.1.1-2), parallelly(v.1.45.0), svglite(v.2.2.1), codetools(v.0.2-20), xml2(v.1.3.8), tidyselect(v.1.2.1), aplot(v.0.2.5), farver(v.2.1.2), matrixStats(v.1.5.0), stats4(v.4.3.2), jsonlite(v.2.0.0), Formula(v.1.2-5), iterators(v.1.0.14), emmeans(v.1.11.1), systemfonts(v.1.2.3), foreach(v.1.5.2), tools(v.4.3.2), treeio(v.1.26.0), ragg(v.1.4.0), glue(v.1.8.0), mnormt(v.2.1.1), gridExtra(v.2.3), xfun(v.0.52), distributional(v.0.5.0), withr(v.3.0.2), numDeriv(v.2016.8-1.1), combinat(v.0.0-8), fastmap(v.1.2.0), callr(v.3.7.6), digest(v.0.6.37), timechange(v.0.3.0), R6(v.2.6.1), gridGraphics(v.0.5-1), estimability(v.1.5.1), colorspace(v.2.1-1), textshaping(v.1.0.1), utf8(v.1.2.5), generics(v.0.1.4), data.table(v.1.17.4), clusterGeneration(v.1.3.8), httr(v.1.4.7), htmlwidgets(v.1.6.4), scatterplot3d(v.0.3-44), pkgconfig(v.2.0.3), gtable(v.0.3.6), htmltools(v.0.5.8.1), carData(v.3.0-5), scales(v.1.4.0), png(v.0.1-8), ggfun(v.0.1.8), rstudioapi(v.0.17.1), reshape2(v.1.4.4), tzdb(v.0.5.0), curl(v.6.2.3), coda(v.0.19-4.1), checkmate(v.2.3.2), nlme(v.3.1-168), cachem(v.1.1.0), DEoptim(v.2.2-8), parallel(v.4.3.2), desc(v.1.4.3), pillar(v.1.10.2), grid(v.4.3.2), vctrs(v.0.6.5), car(v.3.1-3), arrayhelpers(v.1.1-0), xtable(v.1.8-4), evaluate(v.1.0.4), mvtnorm(v.1.3-3), cli(v.3.6.5), compiler(v.4.3.2), rlang(v.1.1.6), rstantools(v.2.4.0), ggsignif(v.0.6.4), labeling(v.0.4.3), ps(v.1.9.1), plyr(v.1.8.9), fs(v.1.6.6), pander(v.0.6.6), stringi(v.1.8.7), QuickJSR(v.1.7.0), lazyeval(v.0.2.2), optimParallel(v.1.0-2), V8(v.6.0.4), Brobdingnag(v.1.2-9), Matrix(v.1.6-1.1), hms(v.1.1.3), clipr(v.0.8.0), igraph(v.2.1.4), RcppParallel(v.5.1.10), bslib(v.0.9.0), phangorn(v.2.12.1) and fastmatch(v.1.1-6)